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Popular >

derivative of (9x+2)^{2/3}

Solution

derivative of

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

Solution

\frac{6}{( 9 x + 2 ) ^{\frac{1}{3}}}

Solution steps

\frac{d}{d x} ((9 x + 2)^{\frac{2}{3}})

Apply the chain rule:

\frac{2}{3 ( 9 x + 2 ) ^{\frac{1}{3}}} \frac{d}{d x} (9 x + 2)

= \frac{2}{3 ( 9 x + 2 ) ^{\frac{1}{3}}} \frac{d}{d x} (9 x + 2)

\frac{d}{d x} (9 x + 2) = 9

= \frac{2}{3 ( 9 x + 2 ) ^{\frac{1}{3}}} \cdot 9

Simplify

\frac{2}{3 ( 9 x + 2 ) ^{\frac{1}{3}}} \cdot 9 : \frac{6}{( 9 x + 2 ) ^{\frac{1}{3}}}

= \frac{6}{( 9 x + 2 ) ^{\frac{1}{3}}}

Popular Examples

integral of (4x+2)(x-1)

\int (4 x + 2) (x - 1) d x

y^{^{'}} + y = 5 x y^{3}

integral of 1/(1-t)

\int \frac{1}{1 - t} d t

limit as x approaches 1 of e^{x^5-x}

x \to 1 lim (e^{x^{5} - x})

f^'(x)=((6tan(x)+2))/(sec(x))

f^{^{'}} (x) = \frac{( 6 tan ( x ) + 2 )}{sec ( x )}

Frequently Asked Questions (FAQ)

What is the derivative of (9x+2)^{2/3} ?
The derivative of (9x+2)^{2/3} is 6/((9x+2)^{1/3)}
What is the first derivative of (9x+2)^{2/3} ?
The first derivative of (9x+2)^{2/3} is 6/((9x+2)^{1/3)}