Mister Exam
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- Derivative of a implicit defined function
- Derivative of Parametric Function
- Partial derivative of the function
- Curve tracing functions Step by Step
- Integral Step by Step
- Differential equations Step by Step
- Limits Step by Step
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How to use it?
- Derivative of:
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Derivative of e^x/x^2
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Derivative of 7x
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Derivative of -(3*pi*cos(pi*t/6))/2
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Derivative of 2^x+1
- Integral of d{x}:
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cos^3x
- Equation:
- cos^3x
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Identical expressions
- y=cos^3x
- y equally co sinus of e of cubed x
- y=cos3x
- y=cos³x
- y=cos to the power of 3x
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Similar expressions
- e^(cos^3*x^7)*arctg*7*x^5
- cos^3*x
- 8sin^2(x)cos^3(x)
Derivative of y=cos^3x
The solution
You have entered
[src]
3 cos (x)
$$\cos^{3}{\left(x \right)}$$
d / 3 \ --\cos (x)/ dx
$$\frac{d}{d x} \cos^{3}{\left(x \right)}$$
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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2 -3*cos (x)*sin(x)
$$- 3 \sin{\left(x \right)} \cos^{2}{\left(x \right)}$$
The second derivative
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/ 2 2 \ 3*\- cos (x) + 2*sin (x)/*cos(x)
$$3 \cdot \left(2 \sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \cos{\left(x \right)}$$
The third derivative
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/ 2 2 \ 3*\- 2*sin (x) + 7*cos (x)/*sin(x)
$$3 \left(- 2 \sin^{2}{\left(x \right)} + 7 \cos^{2}{\left(x \right)}\right) \sin{\left(x \right)}$$
The graph