Mister Exam
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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 x^2-2
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Derivative of cos^4x
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Derivative of sh(x)
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Derivative of y=x^3-3x^2+6x-10
- Graphing y =:
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cos^4x
- Integral of d{x}:
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cos^4x
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Identical expressions
- cos^4x
- co sinus of e of to the power of 4x
- cos4x
- cos⁴x
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Similar expressions
- y=sin^4(x)cos^4(x)
- cos^4(x)
- sin^4(x)*cos^4(x)
Derivative of cos^4x
The solution
You have entered
[src]
4 cos (x)
$$\cos^{4}{\left(x \right)}$$
d / 4 \ --\cos (x)/ dx
$$\frac{d}{d x} \cos^{4}{\left(x \right)}$$
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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The answer is:
The first derivative
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3 -4*cos (x)*sin(x)
$$- 4 \sin{\left(x \right)} \cos^{3}{\left(x \right)}$$
The second derivative
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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
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/ 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