Mister Exam
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- Derivative of a implicit defined function
- Derivative of Parametric Function
- Partial derivative of the function
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How to use it?
- Derivative of:
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Derivative of y=2x+3
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Derivative of ln(x+5)^5
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Derivative of (x^2-x)/2
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Derivative of sin^2x^2
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Identical expressions
- sin^ two x^2
- sinus of squared x squared
- sinus of to the power of two x squared
- sin2x2
- sin²x²
- sin to the power of 2x to the power of 2
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Similar expressions
- sin^(2)(x^2-3)
Derivative of sin^2x^2
The solution
You have entered
[src]
/ 2\
\2 /
(sin(x))
$$\sin^{2^{2}}{\left(x \right)}$$
/ / 2\\ d | \2 /| --\(sin(x)) / dx
$$\frac{d}{d x} \sin^{2^{2}}{\left(x \right)}$$
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\
\2 /
4*(sin(x)) *cos(x)
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sin(x)
$$\frac{4 \sin^{2^{2}}{\left(x \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}}$$
The second derivative
[src]
2 / 2 2 \ 4*sin (x)*\- sin (x) + 3*cos (x)/
$$4 \left(- \sin^{2}{\left(x \right)} + 3 \cos^{2}{\left(x \right)}\right) \sin^{2}{\left(x \right)}$$
The third derivative
[src]
/ 2 2 \ 8*\- 5*sin (x) + 3*cos (x)/*cos(x)*sin(x)
$$8 \left(- 5 \sin^{2}{\left(x \right)} + 3 \cos^{2}{\left(x \right)}\right) \sin{\left(x \right)} \cos{\left(x \right)}$$
The graph