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
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How to use it?
- Derivative of:
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Derivative of 4/x^3
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Derivative of (x+3)^2*(x+5)-1
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Derivative of x^3+2
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Derivative of x^(-2)
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Identical expressions
- sin(t)^(three)
- sinus of (t) to the power of (3)
- sinus of (t) to the power of (three)
- sin(t)(3)
- sint3
- sint^3
Derivative of sin(t)^(3)
The solution
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3 sin (t)
$$\sin^{3}{\left(t \right)}$$
d / 3 \ --\sin (t)/ dt
$$\frac{d}{d t} \sin^{3}{\left(t \right)}$$
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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/ 2 2 \ 3*\- sin (t) + 2*cos (t)/*sin(t)
$$3 \left(- \sin^{2}{\left(t \right)} + 2 \cos^{2}{\left(t \right)}\right) \sin{\left(t \right)}$$
The third derivative
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/ 2 2 \ 3*\- 7*sin (t) + 2*cos (t)/*cos(t)
$$3 \left(- 7 \sin^{2}{\left(t \right)} + 2 \cos^{2}{\left(t \right)}\right) \cos{\left(t \right)}$$
The graph