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 sin(x)
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Derivative of arcctg(x)
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Derivative of sec²x
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Derivative of cos^2x^2
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Identical expressions
- cos^ two x^2
- co sinus of e of squared x squared
- co sinus of e of to the power of two x squared
- cos2x2
- cos²x²
- cos to the power of 2x to the power of 2
Derivative of cos^2x^2
The solution
You have entered
[src]
/ 2\
\2 /
(cos(x))
$$\cos^{2^{2}}{\left(x \right)}$$
/ / 2\\ d | \2 /| --\(cos(x)) / dx
$$\frac{d}{d x} \cos^{2^{2}}{\left(x \right)}$$
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 cosine is negative sine:
The result of the chain rule is:
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Now simplify:
The answer is:
The first derivative
[src]
/ 2\
\2 /
-4*(cos(x)) *sin(x)
----------------------
cos(x)
$$- \frac{4 \sin{\left(x \right)} \cos^{2^{2}}{\left(x \right)}}{\cos{\left(x \right)}}$$
The second derivative
[src]
2 / 2 2 \ 4*cos (x)*\- cos (x) + 3*sin (x)/
$$4 \cdot \left(3 \sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \cos^{2}{\left(x \right)}$$
The third derivative
[src]
/ 2 2 \ 8*\- 3*sin (x) + 5*cos (x)/*cos(x)*sin(x)
$$8 \left(- 3 \sin^{2}{\left(x \right)} + 5 \cos^{2}{\left(x \right)}\right) \sin{\left(x \right)} \cos{\left(x \right)}$$
The graph