Mister Exam
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How to use it?
- Derivative of:
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Derivative of cos(x)^(25)
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Derivative of ch(x)
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Derivative of tgx^2
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Derivative of sqrt(x^2-25)
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Identical expressions
- cos(x)^(twenty-five)
- co sinus of e of (x) to the power of (25)
- co sinus of e of (x) to the power of (twenty minus five)
- cos(x)(25)
- cosx25
- cosx^25
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Similar expressions
- cosx^(25)
Derivative of cos(x)^(25)
The solution
You have entered
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25 cos (x)
$$\cos^{25}{\left(x \right)}$$
d / 25 \ --\cos (x)/ dx
$$\frac{d}{d x} \cos^{25}{\left(x \right)}$$
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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24 -25*cos (x)*sin(x)
$$- 25 \sin{\left(x \right)} \cos^{24}{\left(x \right)}$$
The second derivative
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23 / 2 2 \ 25*cos (x)*\- cos (x) + 24*sin (x)/
$$25 \cdot \left(24 \sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \cos^{23}{\left(x \right)}$$
The third derivative
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22 / 2 2 \ 25*cos (x)*\- 552*sin (x) + 73*cos (x)/*sin(x)
$$25 \left(- 552 \sin^{2}{\left(x \right)} + 73 \cos^{2}{\left(x \right)}\right) \sin{\left(x \right)} \cos^{22}{\left(x \right)}$$
The graph