Mister Exam
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- Derivative of a implicit defined function
- Derivative of Parametric Function
- Partial derivative of the function
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How to use it?
- Derivative of:
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Derivative of e^-1
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Derivative of 2*x^5
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Derivative of sin(2*x^2+3)
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Derivative of f(x)=5
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Identical expressions
- (3x)^ one / four
- (3x) to the power of 1 divide by 4
- (3x) to the power of one divide by four
- (3x)1/4
- 3x1/4
- 3x^1/4
- (3x)^1 divide by 4
Derivative of (3x)^1/4
The solution
You have entered
[src]
4 _____ \/ 3*x
$$\sqrt[4]{3 x}$$
d /4 _____\ --\\/ 3*x / dx
$$\frac{d}{d x} \sqrt[4]{3 x}$$
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 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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The result of the chain rule is:
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The answer is:
The first derivative
[src]
4 ___ 4 ___
\/ 3 *\/ x
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4*x
$$\frac{\sqrt[4]{3} \sqrt[4]{x}}{4 x}$$
The second derivative
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4 ___
-3*\/ 3
--------
7/4
16*x
$$- \frac{3 \cdot \sqrt[4]{3}}{16 x^{\frac{7}{4}}}$$
The third derivative
[src]
4 ___
21*\/ 3
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11/4
64*x
$$\frac{21 \cdot \sqrt[4]{3}}{64 x^{\frac{11}{4}}}$$
The graph