What is the derivative of (4x+8)^{1/3} ?

The derivative of (4x+8)^{1/3} is 4/(3(4x+8)^{2/3)}

What is the first derivative of (4x+8)^{1/3} ?

The first derivative of (4x+8)^{1/3} is 4/(3(4x+8)^{2/3)}

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derivative of

(4 x + 8)^{\frac{1}{3}}

\frac{4}{3 ( 4 x + 8 ) ^{\frac{2}{3}}}

Solution steps

\frac{d}{d x} ((4 x + 8)^{\frac{1}{3}})

Apply the chain rule:

\frac{1}{3 ( 4 x + 8 ) ^{\frac{2}{3}}} \frac{d}{d x} (4 x + 8)

= \frac{1}{3 ( 4 x + 8 ) ^{\frac{2}{3}}} \frac{d}{d x} (4 x + 8)

\frac{d}{d x} (4 x + 8) = 4

= \frac{1}{3 ( 4 x + 8 ) ^{\frac{2}{3}}} \cdot 4

Simplify

\frac{1}{3 ( 4 x + 8 ) ^{\frac{2}{3}}} \cdot 4 : \frac{4}{3 ( 4 x + 8 ) ^{\frac{2}{3}}}

= \frac{4}{3 ( 4 x + 8 ) ^{\frac{2}{3}}}

e^{x} + 2 y

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

\frac{d}{d a} (\frac{( 1 + 2 cos ^{2} ( a ) )}{( 1 + 3 cot ^{2} ( a ) )})

\frac{- x ^{4}}{2}

y = x y + 10 x + 10 y

What is the derivative of (4x+8)^{1/3} ?
The derivative of (4x+8)^{1/3} is 4/(3(4x+8)^{2/3)}
What is the first derivative of (4x+8)^{1/3} ?
The first derivative of (4x+8)^{1/3} is 4/(3(4x+8)^{2/3)}