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 a^3
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Derivative of y=sin^5*x
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Derivative of x*e^(-x)
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Derivative of x^4-2x^3
- Integral of d{x}:
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sin^5*x
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Identical expressions
- y=sin^ five *x
- y equally sinus of to the power of 5 multiply by x
- y equally sinus of to the power of five multiply by x
- y=sin5*x
- y=sin⁵*x
- y=sin^5x
- y=sin5x
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Similar expressions
- 2*sin^5(x)
- y=tg^5(x^0.5)*sin^5(x^0.5)+3(tg(x)*sin(x))^0.5
- sin^5(x)+cos^5(x)
- y=sin^5(x/4)
Derivative of y=sin^5*x
The solution
You have entered
[src]
5 sin (x)
$$\sin^{5}{\left(x \right)}$$
d / 5 \ --\sin (x)/ dx
$$\frac{d}{d x} \sin^{5}{\left(x \right)}$$
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 sine is cosine:
The result of the chain rule is:
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The answer is:
The second derivative
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3 / 2 2 \ 5*sin (x)*\- sin (x) + 4*cos (x)/
$$5 \left(- \sin^{2}{\left(x \right)} + 4 \cos^{2}{\left(x \right)}\right) \sin^{3}{\left(x \right)}$$
The third derivative
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2 / 2 2 \ 5*sin (x)*\- 13*sin (x) + 12*cos (x)/*cos(x)
$$5 \left(- 13 \sin^{2}{\left(x \right)} + 12 \cos^{2}{\left(x \right)}\right) \sin^{2}{\left(x \right)} \cos{\left(x \right)}$$
The graph