Mister Exam
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- Derivative of a implicit defined function
- Derivative of Parametric Function
- Partial derivative of the function
- Curve tracing functions Step by Step
- Integral Step by Step
- Differential equations Step by Step
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How to use it?
- Derivative of:
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Derivative of sin(4x)
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Derivative of y=cos9x
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Derivative of log(x+(1+x^2)^(1/2))
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Derivative of e^sin^2(3x)
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Identical expressions
- log(sin(x^ three), two)
- logarithm of ( sinus of (x cubed ),2)
- logarithm of ( sinus of (x to the power of three), two)
- log(sin(x3),2)
- logsinx3,2
- log(sin(x³),2)
- log(sin(x to the power of 3),2)
- logsinx^3,2
Derivative of log(sin(x^3),2)
The solution
You have entered
[src]
/ / 3\ \ log\sin\x /, 2/
$$\log{\left(\sin{\left(x^{3} \right)} \right)}$$
log(sin(x^3), 2)
The first derivative
[src]
2 / 3\
3*x *cos\x /
------------
/ 3\
sin\x /
$$\frac{3 x^{2} \cos{\left(x^{3} \right)}}{\sin{\left(x^{3} \right)}}$$
The second derivative
[src]
/ / 3\ 3 2/ 3\\
| 3 2*cos\x / 3*x *cos \x /|
3*x*|- 3*x + --------- - -------------|
| / 3\ 2/ 3\ |
\ sin\x / sin \x / /
$$3 x \left(- 3 x^{3} - \frac{3 x^{3} \cos^{2}{\left(x^{3} \right)}}{\sin^{2}{\left(x^{3} \right)}} + \frac{2 \cos{\left(x^{3} \right)}}{\sin{\left(x^{3} \right)}}\right)$$
The third derivative
[src]
/ / 3\ 3 2/ 3\ 6 3/ 3\ 6 / 3\\ | 3 cos\x / 9*x *cos \x / 9*x *cos \x / 9*x *cos\x /| 6*|- 9*x + ------- - ------------- + ------------- + ------------| | / 3\ 2/ 3\ 3/ 3\ / 3\ | \ sin\x / sin \x / sin \x / sin\x / /
$$6 \left(\frac{9 x^{6} \cos{\left(x^{3} \right)}}{\sin{\left(x^{3} \right)}} + \frac{9 x^{6} \cos^{3}{\left(x^{3} \right)}}{\sin^{3}{\left(x^{3} \right)}} - 9 x^{3} - \frac{9 x^{3} \cos^{2}{\left(x^{3} \right)}}{\sin^{2}{\left(x^{3} \right)}} + \frac{\cos{\left(x^{3} \right)}}{\sin{\left(x^{3} \right)}}\right)$$