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)}

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\frac{d}{d x} ((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}}}

\int (\frac{3}{x} + 3 x) d x

\frac{d}{d x} (x (cos (x)))

9 x^{2} - 1

\int \frac{e ^{3 x}}{2} d x

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)}