What is the derivative of f(x)=4(x-3)^{2/3} ?

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

What is the first derivative of f(x)=4(x-3)^{2/3} ?

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

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derivative of

f (x) = 4 (x - 3)^{\frac{2}{3}}

\frac{8}{3 ( x - 3 ) ^{\frac{1}{3}}}

Solution steps

\frac{d}{d x} (4 (x - 3)^{\frac{2}{3}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 4 \frac{d}{d x} ((x - 3)^{\frac{2}{3}})

Apply the chain rule:

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

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

\frac{d}{d x} (x - 3) = 1

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

Simplify

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

= \frac{8}{3 ( x - 3 ) ^{\frac{1}{3}}}

\frac{d}{d x} (arctan (\frac{c}{x}))

f (x) = \frac{5 x}{x - 2}, at x = 3

\frac{d}{d x} (16 e^{- 2 x})

n = 3 \sum \infty \frac{3}{2} \cdot \frac{1}{4 ^{n}}

\int_{0}^{8} f (x) d x

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