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 x^-6
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Derivative of f(x)=1
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Derivative of e^x*x^2
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Derivative of 2*sqrt(x^3)
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Identical expressions
- four *(x^ two ^(one / three))
- 4 multiply by (x squared to the power of (1 divide by 3))
- four multiply by (x to the power of two to the power of (one divide by three))
- 4*(x2(1/3))
- 4*x21/3
- 4*(x²^(1/3))
- 4*(x to the power of 2 to the power of (1/3))
- 4(x^2^(1/3))
- 4(x2(1/3))
- 4x21/3
- 4x^2^1/3
- 4*(x^2^(1 divide by 3))
Derivative of 4*(x^2^(1/3))
The solution
You have entered
[src]
3 ___ \/ 2 4*x
$$4 x^{\sqrt[3]{2}}$$
/ 3 ___\ d | \/ 2 | --\4*x / dx
$$\frac{d}{d x} 4 x^{\sqrt[3]{2}}$$
Detail solution
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The derivative of a constant times a function is the constant times the derivative of the function.
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Apply the power rule: goes to
So, the result is:
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Now simplify:
The answer is:
The first derivative
[src]
3 ___
3 ___ \/ 2
4*\/ 2 *x
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x
$$\frac{4 \cdot \sqrt[3]{2} x^{\sqrt[3]{2}}}{x}$$
The second derivative
[src]
3 ___
3 ___ \/ 2 / 3 ___\
-4*\/ 2 *x *\1 - \/ 2 /
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2
x
$$- \frac{4 \cdot \sqrt[3]{2} x^{\sqrt[3]{2}} \cdot \left(- \sqrt[3]{2} + 1\right)}{x^{2}}$$
The third derivative
[src]
3 ___
\/ 2 / 2/3 3 ___\
4*x *\2 - 3*2 + 2*\/ 2 /
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3
x
$$\frac{4 x^{\sqrt[3]{2}} \left(- 3 \cdot 2^{\frac{2}{3}} + 2 + 2 \cdot \sqrt[3]{2}\right)}{x^{3}}$$
The graph