What is the derivative of (2x+5)^{1/3} ?

The derivative of (2x+5)^{1/3} is 2/(3(2x+5)^{2/3)}

What is the first derivative of (2x+5)^{1/3} ?

The first derivative of (2x+5)^{1/3} is 2/(3(2x+5)^{2/3)}

Popular >

derivative of

(2 x + 5)^{\frac{1}{3}}

\frac{2}{3 ( 2 x + 5 ) ^{\frac{2}{3}}}

Solution steps

\frac{d}{d x} ((2 x + 5)^{\frac{1}{3}})

Apply the chain rule:

\frac{1}{3 ( 2 x + 5 ) ^{\frac{2}{3}}} \frac{d}{d x} (2 x + 5)

= \frac{1}{3 ( 2 x + 5 ) ^{\frac{2}{3}}} \frac{d}{d x} (2 x + 5)

\frac{d}{d x} (2 x + 5) = 2

= \frac{1}{3 ( 2 x + 5 ) ^{\frac{2}{3}}} \cdot 2

Simplify

\frac{1}{3 ( 2 x + 5 ) ^{\frac{2}{3}}} \cdot 2 : \frac{2}{3 ( 2 x + 5 ) ^{\frac{2}{3}}}

= \frac{2}{3 ( 2 x + 5 ) ^{\frac{2}{3}}}

2 x^{3} - 4 x^{5} + 8 + 7 x^{2}

\frac{- 1}{t ^{2}}

e^{\frac{- 1}{x ^{2}}}

\frac{1}{( x ^{2} + y ^{2} )}

(\frac{x + 1}{x})^{3}

What is the derivative of (2x+5)^{1/3} ?
The derivative of (2x+5)^{1/3} is 2/(3(2x+5)^{2/3)}
What is the first derivative of (2x+5)^{1/3} ?
The first derivative of (2x+5)^{1/3} is 2/(3(2x+5)^{2/3)}