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

The derivative of x(2x+9^{1/3}) is (8x+27)/(3(2x+9)^{2/3)}

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

The first derivative of x(2x+9^{1/3}) is (8x+27)/(3(2x+9)^{2/3)}

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

\frac{8 x + 27}{3 ( 2 x + 9 ) ^{\frac{2}{3}}}

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = (2 x + 9)^{\frac{1}{3}}

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

\frac{d x}{d x} = 1

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

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

Simplify

1 \cdot (2 x + 9)^{\frac{1}{3}} + \frac{2}{3 ( 2 x + 9 ) ^{\frac{2}{3}}} x : \frac{8 x + 27}{3 ( 2 x + 9 ) ^{\frac{2}{3}}}

= \frac{8 x + 27}{3 ( 2 x + 9 ) ^{\frac{2}{3}}}

\int_{0}^{\infty} t e^{- k t} d t

\int \frac{x}{x ^{2} + 2 x + 1} d x

\frac{d}{d x} (2 x^{2} - 4)

\frac{d}{d x} (ln x^{2} - 4)

f (x) = - 2 x^{2} - 12 x - 4

What is the derivative of x(2x+9^{1/3}) ?
The derivative of x(2x+9^{1/3}) is (8x+27)/(3(2x+9)^{2/3)}
What is the first derivative of x(2x+9^{1/3}) ?
The first derivative of x(2x+9^{1/3}) is (8x+27)/(3(2x+9)^{2/3)}