Mister Exam
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- Derivative of a implicit defined function
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How to use it?
- Derivative of:
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Derivative of sin³x²
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Derivative of (2x+3)^100
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Derivative of dy^2/dx
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Derivative of y=3x^4-2x^2+x-5
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Identical expressions
- sin³x²
- sinus of ³x²
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Similar expressions
- y=sin³(x²+2x)
- y=sin³(x²-4x)
Derivative of sin³x²
The solution
You have entered
[src]
/ 2\
\3 /
(sin(x))
$$\sin^{3^{2}}{\left(x \right)}$$
/ / 2\\ d | \3 /| --\(sin(x)) / dx
$$\frac{d}{d x} \sin^{3^{2}}{\left(x \right)}$$
Detail solution
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Let .
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Apply the power rule: goes to
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Then, apply the chain rule. Multiply by :
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The derivative of sine is cosine:
The result of the chain rule is:
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Now simplify:
The answer is:
The first derivative
[src]
/ 2\
\3 /
9*(sin(x)) *cos(x)
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sin(x)
$$\frac{9 \sin^{3^{2}}{\left(x \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}}$$
The second derivative
[src]
7 / 2 2 \ 9*sin (x)*\- sin (x) + 8*cos (x)/
$$9 \left(- \sin^{2}{\left(x \right)} + 8 \cos^{2}{\left(x \right)}\right) \sin^{7}{\left(x \right)}$$
The third derivative
[src]
6 / 2 2 \ 9*sin (x)*\- 25*sin (x) + 56*cos (x)/*cos(x)
$$9 \left(- 25 \sin^{2}{\left(x \right)} + 56 \cos^{2}{\left(x \right)}\right) \sin^{6}{\left(x \right)} \cos{\left(x \right)}$$
The graph