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Popular >

derivative of (4x+5)^{1/5}

Solution

derivative of

(4 x + 5)^{\frac{1}{5}}

Solution

\frac{4}{5 ( 4 x + 5 ) ^{\frac{4}{5}}}

Solution steps

\frac{d}{d x} ((4 x + 5)^{\frac{1}{5}})

Apply the chain rule:

\frac{1}{5 ( 4 x + 5 ) ^{\frac{4}{5}}} \frac{d}{d x} (4 x + 5)

= \frac{1}{5 ( 4 x + 5 ) ^{\frac{4}{5}}} \frac{d}{d x} (4 x + 5)

\frac{d}{d x} (4 x + 5) = 4

= \frac{1}{5 ( 4 x + 5 ) ^{\frac{4}{5}}} \cdot 4

Simplify

\frac{1}{5 ( 4 x + 5 ) ^{\frac{4}{5}}} \cdot 4 : \frac{4}{5 ( 4 x + 5 ) ^{\frac{4}{5}}}

= \frac{4}{5 ( 4 x + 5 ) ^{\frac{4}{5}}}

Popular Examples

derivative of arccos(x/5)derivative of

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integral of (4x)/(x^2+5)

\int \frac{4 x}{x ^{2} + 5} d x

(x^2+xy-y^2)dx+xydy=0

(x^{2} + x y - y^{2}) d x + x y d y = 0

limit as x approaches 0 of (x-3)sqrt(x)

x \to 0 lim ((x - 3) x)

derivative of sin^5(3x^2-x+13)derivative of

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Frequently Asked Questions (FAQ)

What is the derivative of (4x+5)^{1/5} ?
The derivative of (4x+5)^{1/5} is 4/(5(4x+5)^{4/5)}
What is the first derivative of (4x+5)^{1/5} ?
The first derivative of (4x+5)^{1/5} is 4/(5(4x+5)^{4/5)}