What is the derivative of (18/(\sqrt[3]{x-2)}) ?

The derivative of (18/(\sqrt[3]{x-2)}) is -6/((x-2)^{4/3)}

What is the first derivative of (18/(\sqrt[3]{x-2)}) ?

The first derivative of (18/(\sqrt[3]{x-2)}) is -6/((x-2)^{4/3)}

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- \frac{6}{( x - 2 ) ^{\frac{4}{3}}}

Solution steps

Take the constant out:

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= 18 \frac{d}{d x} ((x - 2)^{- \frac{1}{3}})

Apply the chain rule:

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

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

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

= 18 (- \frac{1}{3 ( x - 2 ) ^{\frac{4}{3}}} \cdot 1)

Simplify

18 (- \frac{1}{3 ( x - 2 ) ^{\frac{4}{3}}} \cdot 1) : - \frac{6}{( x - 2 ) ^{\frac{4}{3}}}

= - \frac{6}{( x - 2 ) ^{\frac{4}{3}}}

x \to 7 lim (\frac{x}{x ^{2} - 49})

sin^{2} (9)

s^{- 2}

\int_{0}^{3} \frac{4 t}{( t - 4 ) ^{2}} d t

\int \frac{1}{x} sin (x) d x

What is the derivative of (18/(\sqrt[3]{x-2)}) ?
The derivative of (18/(\sqrt[3]{x-2)}) is -6/((x-2)^{4/3)}
What is the first derivative of (18/(\sqrt[3]{x-2)}) ?
The first derivative of (18/(\sqrt[3]{x-2)}) is -6/((x-2)^{4/3)}