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 y=7x+x^4
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Derivative of sinx^3
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Derivative of f(x)=2x^3
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Derivative of y=tanh(1-3x)
- Integral of d{x}:
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sinx^3
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Identical expressions
- sinx^ three
- sinus of x cubed
- sinus of x to the power of three
- sinx3
- sinx³
- sinx to the power of 3
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Similar expressions
- y=x^sin*x^3
- x^(sin(x^3))
- sin(3*x)+sin(x)^(3)
Derivative of sinx^3
The solution
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3 sin (x)
$$\sin^{3}{\left(x \right)}$$
d / 3 \ --\sin (x)/ dx
$$\frac{d}{d x} \sin^{3}{\left(x \right)}$$
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 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 (x) + 2*cos (x)/*sin(x)
$$3 \left(- \sin^{2}{\left(x \right)} + 2 \cos^{2}{\left(x \right)}\right) \sin{\left(x \right)}$$
The third derivative
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/ 2 2 \ 3*\- 7*sin (x) + 2*cos (x)/*cos(x)
$$3 \left(- 7 \sin^{2}{\left(x \right)} + 2 \cos^{2}{\left(x \right)}\right) \cos{\left(x \right)}$$
The graph