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- Derivative of a implicit defined function
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- Partial derivative of the function
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How to use it?
- Derivative of:
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Derivative of -2x/(1+x^2)^2
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Derivative of (x^2+49)/x
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Derivative of 2*x-x^2
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Derivative of x*e^x-e^x
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Identical expressions
- (sin(five *x))^(log(two *x- three))
- ( sinus of (5 multiply by x)) to the power of ( logarithm of (2 multiply by x minus 3))
- ( sinus of (five multiply by x)) to the power of ( logarithm of (two multiply by x minus three))
- (sin(5*x))(log(2*x-3))
- sin5*xlog2*x-3
- (sin(5x))^(log(2x-3))
- (sin(5x))(log(2x-3))
- sin5xlog2x-3
- sin5x^log2x-3
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Similar expressions
- (sin(5*x))^(log(2*x+3))
Derivative of (sin(5*x))^(log(2*x-3))
The solution
You have entered
[src]
log(2*x - 3) sin (5*x)
$$\sin^{\log{\left(2 x - 3 \right)}}{\left(5 x \right)}$$
sin(5*x)^log(2*x - 3)
Detail solution
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Don't know the steps in finding this derivative.
But the derivative is
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Now simplify:
The answer is:
The first derivative
[src]
log(2*x - 3) /2*log(sin(5*x)) 5*cos(5*x)*log(2*x - 3)\
sin (5*x)*|--------------- + -----------------------|
\ 2*x - 3 sin(5*x) /
$$\left(\frac{5 \log{\left(2 x - 3 \right)} \cos{\left(5 x \right)}}{\sin{\left(5 x \right)}} + \frac{2 \log{\left(\sin{\left(5 x \right)} \right)}}{2 x - 3}\right) \sin^{\log{\left(2 x - 3 \right)}}{\left(5 x \right)}$$
The second derivative
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/ 2 2 \
log(-3 + 2*x) |/2*log(sin(5*x)) 5*cos(5*x)*log(-3 + 2*x)\ 4*log(sin(5*x)) 25*cos (5*x)*log(-3 + 2*x) 20*cos(5*x) |
sin (5*x)*||--------------- + ------------------------| - 25*log(-3 + 2*x) - --------------- - -------------------------- + -------------------|
|\ -3 + 2*x sin(5*x) / 2 2 (-3 + 2*x)*sin(5*x)|
\ (-3 + 2*x) sin (5*x) /
$$\left(\left(\frac{5 \log{\left(2 x - 3 \right)} \cos{\left(5 x \right)}}{\sin{\left(5 x \right)}} + \frac{2 \log{\left(\sin{\left(5 x \right)} \right)}}{2 x - 3}\right)^{2} - 25 \log{\left(2 x - 3 \right)} - \frac{25 \log{\left(2 x - 3 \right)} \cos^{2}{\left(5 x \right)}}{\sin^{2}{\left(5 x \right)}} + \frac{20 \cos{\left(5 x \right)}}{\left(2 x - 3\right) \sin{\left(5 x \right)}} - \frac{4 \log{\left(\sin{\left(5 x \right)} \right)}}{\left(2 x - 3\right)^{2}}\right) \sin^{\log{\left(2 x - 3 \right)}}{\left(5 x \right)}$$
The third derivative
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/ 3 / 2 \ 2 3 \
log(-3 + 2*x) |/2*log(sin(5*x)) 5*cos(5*x)*log(-3 + 2*x)\ 150 /2*log(sin(5*x)) 5*cos(5*x)*log(-3 + 2*x)\ | 4*log(sin(5*x)) 20*cos(5*x) 25*cos (5*x)*log(-3 + 2*x)| 16*log(sin(5*x)) 150*cos (5*x) 60*cos(5*x) 250*cos (5*x)*log(-3 + 2*x) 250*cos(5*x)*log(-3 + 2*x)|
sin (5*x)*||--------------- + ------------------------| - -------- - 3*|--------------- + ------------------------|*|25*log(-3 + 2*x) + --------------- - ------------------- + --------------------------| + ---------------- - -------------------- - -------------------- + --------------------------- + --------------------------|
|\ -3 + 2*x sin(5*x) / -3 + 2*x \ -3 + 2*x sin(5*x) / | 2 (-3 + 2*x)*sin(5*x) 2 | 3 2 2 3 sin(5*x) |
\ \ (-3 + 2*x) sin (5*x) / (-3 + 2*x) (-3 + 2*x)*sin (5*x) (-3 + 2*x) *sin(5*x) sin (5*x) /
$$\left(\left(\frac{5 \log{\left(2 x - 3 \right)} \cos{\left(5 x \right)}}{\sin{\left(5 x \right)}} + \frac{2 \log{\left(\sin{\left(5 x \right)} \right)}}{2 x - 3}\right)^{3} - 3 \left(\frac{5 \log{\left(2 x - 3 \right)} \cos{\left(5 x \right)}}{\sin{\left(5 x \right)}} + \frac{2 \log{\left(\sin{\left(5 x \right)} \right)}}{2 x - 3}\right) \left(25 \log{\left(2 x - 3 \right)} + \frac{25 \log{\left(2 x - 3 \right)} \cos^{2}{\left(5 x \right)}}{\sin^{2}{\left(5 x \right)}} - \frac{20 \cos{\left(5 x \right)}}{\left(2 x - 3\right) \sin{\left(5 x \right)}} + \frac{4 \log{\left(\sin{\left(5 x \right)} \right)}}{\left(2 x - 3\right)^{2}}\right) + \frac{250 \log{\left(2 x - 3 \right)} \cos{\left(5 x \right)}}{\sin{\left(5 x \right)}} + \frac{250 \log{\left(2 x - 3 \right)} \cos^{3}{\left(5 x \right)}}{\sin^{3}{\left(5 x \right)}} - \frac{150}{2 x - 3} - \frac{150 \cos^{2}{\left(5 x \right)}}{\left(2 x - 3\right) \sin^{2}{\left(5 x \right)}} - \frac{60 \cos{\left(5 x \right)}}{\left(2 x - 3\right)^{2} \sin{\left(5 x \right)}} + \frac{16 \log{\left(\sin{\left(5 x \right)} \right)}}{\left(2 x - 3\right)^{3}}\right) \sin^{\log{\left(2 x - 3 \right)}}{\left(5 x \right)}$$