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 cos^5x
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Derivative of x^4-2x^2+1
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Derivative of ln(tan(3x))
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Derivative of 4tanx
- Integral of d{x}:
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cos^5x
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Identical expressions
- cos^5x
- co sinus of e of to the power of 5x
- cos5x
- cos⁵x
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Similar expressions
- sin^5(x)+cos^5(x)
Derivative of cos^5x
The solution
You have entered
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5 cos (x)
$$\cos^{5}{\left(x \right)}$$
d / 5 \ --\cos (x)/ dx
$$\frac{d}{d x} \cos^{5}{\left(x \right)}$$
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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4 -5*cos (x)*sin(x)
$$- 5 \sin{\left(x \right)} \cos^{4}{\left(x \right)}$$
The second derivative
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3 / 2 2 \ 5*cos (x)*\- cos (x) + 4*sin (x)/
$$5 \cdot \left(4 \sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \cos^{3}{\left(x \right)}$$
The third derivative
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2 / 2 2 \ 5*cos (x)*\- 12*sin (x) + 13*cos (x)/*sin(x)
$$5 \left(- 12 \sin^{2}{\left(x \right)} + 13 \cos^{2}{\left(x \right)}\right) \sin{\left(x \right)} \cos^{2}{\left(x \right)}$$
The graph