Mister Exam
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How to use it?
- Derivative of:
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Derivative of 2^(3*x)
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Derivative of -2/x
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Derivative of 1/cos(x)
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Derivative of 1/(1-x)
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Identical expressions
- ln(abs(3sinx))+ln(abs(5cosx*sinx))
- ln(abs(3 sinus of x)) plus ln(abs(5 co sinus of e of x multiply by sinus of x))
- ln(abs(3sinx))+ln(abs(5cosxsinx))
- lnabs3sinx+lnabs5cosxsinx
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Similar expressions
- ln(abs(3sinx))-ln(abs(5cosx*sinx))
Derivative of ln(abs(3sinx))+ln(abs(5cosx*sinx))
The solution
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[src]
log(|3*sin(x)|) + log(|5*cos(x)*sin(x)|)
$$\log{\left(\left|{\sin{\left(x \right)} 5 \cos{\left(x \right)}}\right| \right)} + \log{\left(\left|{3 \sin{\left(x \right)}}\right| \right)}$$
log(Abs(3*sin(x))) + log(Abs((5*cos(x))*sin(x)))
The first derivative
[src]
/ 2 2 \
\- 5*sin (x) + 5*cos (x)/*sign(cos(x)*sin(x)) 3*cos(x)*sign(sin(x))
--------------------------------------------- + ---------------------
|5*cos(x)*sin(x)| |3*sin(x)|
$$\frac{\left(- 5 \sin^{2}{\left(x \right)} + 5 \cos^{2}{\left(x \right)}\right) \operatorname{sign}{\left(\sin{\left(x \right)} \cos{\left(x \right)} \right)}}{\left|{\sin{\left(x \right)} 5 \cos{\left(x \right)}}\right|} + \frac{3 \cos{\left(x \right)} \operatorname{sign}{\left(\sin{\left(x \right)} \right)}}{\left|{3 \sin{\left(x \right)}}\right|}$$
The second derivative
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2 2
2 2 / 2 2 \ 2 / 2 2 \ 2
cos (x)*sign (sin(x)) 3*sign(sin(x))*sin(x) 2*\sin (x) - cos (x)/ *DiracDelta(cos(x)*sin(x)) 6*cos (x)*DiracDelta(sin(x)) \sin (x) - cos (x)/ *sign (cos(x)*sin(x)) 4*cos(x)*sign(cos(x)*sin(x))*sin(x)
- --------------------- - --------------------- + ------------------------------------------------ + ---------------------------- - ----------------------------------------- - -----------------------------------
2 |3*sin(x)| |cos(x)*sin(x)| |3*sin(x)| 2 2 |cos(x)*sin(x)|
sin (x) cos (x)*sin (x)
$$\frac{2 \left(\sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right)^{2} \delta\left(\sin{\left(x \right)} \cos{\left(x \right)}\right)}{\left|{\sin{\left(x \right)} \cos{\left(x \right)}}\right|} - \frac{\left(\sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right)^{2} \operatorname{sign}^{2}{\left(\sin{\left(x \right)} \cos{\left(x \right)} \right)}}{\sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}} - \frac{4 \sin{\left(x \right)} \cos{\left(x \right)} \operatorname{sign}{\left(\sin{\left(x \right)} \cos{\left(x \right)} \right)}}{\left|{\sin{\left(x \right)} \cos{\left(x \right)}}\right|} - \frac{3 \sin{\left(x \right)} \operatorname{sign}{\left(\sin{\left(x \right)} \right)}}{\left|{3 \sin{\left(x \right)}}\right|} + \frac{6 \cos^{2}{\left(x \right)} \delta\left(\sin{\left(x \right)}\right)}{\left|{3 \sin{\left(x \right)}}\right|} - \frac{\cos^{2}{\left(x \right)} \operatorname{sign}^{2}{\left(\sin{\left(x \right)} \right)}}{\sin^{2}{\left(x \right)}}$$
The third derivative
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3 2 2 3
2 / 2 2 \ 3 2 2 2 3 2 / 2 2 \ 3 / 2 2 \ 2 / 2 2 \ 2 / 2 2 \ / 2 2 \
4*cos (x)*sign(cos(x)*sin(x)) 3*cos(x)*sign(sin(x)) 2*\sin (x) - cos (x)/ *DiracDelta(cos(x)*sin(x), 1) 2*cos (x)*sign (sin(x)) 3*sign (sin(x))*cos(x) 4*sin (x)*sign(cos(x)*sin(x)) 6*cos (x)*DiracDelta(sin(x), 1) 18*DiracDelta(sin(x))*cos(x)*sin(x) 12*sign (cos(x)*sin(x))*\sin (x) - cos (x)/ 6*cos (x)*DiracDelta(sin(x))*sign(sin(x)) 2*\sin (x) - cos (x)/ *sign (cos(x)*sin(x)) 2*\sin (x) - cos (x)/ *sign (cos(x)*sin(x)) 6*\sin (x) - cos (x)/ *DiracDelta(cos(x)*sin(x))*sign(cos(x)*sin(x)) 24*\sin (x) - cos (x)/*DiracDelta(cos(x)*sin(x))*cos(x)*sin(x)
- ----------------------------- - --------------------- - --------------------------------------------------- + ----------------------- + ---------------------- + ----------------------------- + ------------------------------- - ----------------------------------- - ------------------------------------------- - ----------------------------------------- - ------------------------------------------- + ------------------------------------------- + -------------------------------------------------------------------- + --------------------------------------------------------------
|cos(x)*sin(x)| |3*sin(x)| |cos(x)*sin(x)| 3 sin(x) |cos(x)*sin(x)| |3*sin(x)| |3*sin(x)| cos(x)*sin(x) 2 3 3 2 2 |cos(x)*sin(x)|
sin (x) sin (x) cos (x)*sin(x) cos(x)*sin (x) cos (x)*sin (x)
$$- \frac{2 \left(\sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right)^{3} \delta^{\left( 1 \right)}\left( \sin{\left(x \right)} \cos{\left(x \right)} \right)}{\left|{\sin{\left(x \right)} \cos{\left(x \right)}}\right|} + \frac{6 \left(\sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right)^{3} \delta\left(\sin{\left(x \right)} \cos{\left(x \right)}\right) \operatorname{sign}{\left(\sin{\left(x \right)} \cos{\left(x \right)} \right)}}{\sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}} - \frac{2 \left(\sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right)^{2} \operatorname{sign}^{2}{\left(\sin{\left(x \right)} \cos{\left(x \right)} \right)}}{\sin{\left(x \right)} \cos^{3}{\left(x \right)}} + \frac{2 \left(\sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right)^{2} \operatorname{sign}^{2}{\left(\sin{\left(x \right)} \cos{\left(x \right)} \right)}}{\sin^{3}{\left(x \right)} \cos{\left(x \right)}} + \frac{24 \left(\sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \sin{\left(x \right)} \cos{\left(x \right)} \delta\left(\sin{\left(x \right)} \cos{\left(x \right)}\right)}{\left|{\sin{\left(x \right)} \cos{\left(x \right)}}\right|} - \frac{12 \left(\sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \operatorname{sign}^{2}{\left(\sin{\left(x \right)} \cos{\left(x \right)} \right)}}{\sin{\left(x \right)} \cos{\left(x \right)}} + \frac{4 \sin^{2}{\left(x \right)} \operatorname{sign}{\left(\sin{\left(x \right)} \cos{\left(x \right)} \right)}}{\left|{\sin{\left(x \right)} \cos{\left(x \right)}}\right|} - \frac{18 \sin{\left(x \right)} \cos{\left(x \right)} \delta\left(\sin{\left(x \right)}\right)}{\left|{3 \sin{\left(x \right)}}\right|} + \frac{6 \cos^{3}{\left(x \right)} \delta^{\left( 1 \right)}\left( \sin{\left(x \right)} \right)}{\left|{3 \sin{\left(x \right)}}\right|} - \frac{4 \cos^{2}{\left(x \right)} \operatorname{sign}{\left(\sin{\left(x \right)} \cos{\left(x \right)} \right)}}{\left|{\sin{\left(x \right)} \cos{\left(x \right)}}\right|} - \frac{3 \cos{\left(x \right)} \operatorname{sign}{\left(\sin{\left(x \right)} \right)}}{\left|{3 \sin{\left(x \right)}}\right|} + \frac{3 \cos{\left(x \right)} \operatorname{sign}^{2}{\left(\sin{\left(x \right)} \right)}}{\sin{\left(x \right)}} - \frac{6 \cos^{3}{\left(x \right)} \delta\left(\sin{\left(x \right)}\right) \operatorname{sign}{\left(\sin{\left(x \right)} \right)}}{\sin^{2}{\left(x \right)}} + \frac{2 \cos^{3}{\left(x \right)} \operatorname{sign}^{2}{\left(\sin{\left(x \right)} \right)}}{\sin^{3}{\left(x \right)}}$$