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)}

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derivative of

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

\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}}}

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)}