What is the derivative of 7(x-5)^{2/3} ?

The derivative of 7(x-5)^{2/3} is (14)/(3(x-5)^{1/3)}

What is the first derivative of 7(x-5)^{2/3} ?

The first derivative of 7(x-5)^{2/3} is (14)/(3(x-5)^{1/3)}

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derivative of

7 (x - 5)^{\frac{2}{3}}

\frac{14}{3 ( x - 5 ) ^{\frac{1}{3}}}

Solution steps

\frac{d}{d x} (7 (x - 5)^{\frac{2}{3}})

Take the constant out:

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

= 7 \frac{d}{d x} ((x - 5)^{\frac{2}{3}})

Apply the chain rule:

\frac{2}{3 ( x - 5 ) ^{\frac{1}{3}}} \frac{d}{d x} (x - 5)

= \frac{2}{3 ( x - 5 ) ^{\frac{1}{3}}} \frac{d}{d x} (x - 5)

\frac{d}{d x} (x - 5) = 1

= 7 \cdot \frac{2}{3 ( x - 5 ) ^{\frac{1}{3}}} \cdot 1

Simplify

7 \cdot \frac{2}{3 ( x - 5 ) ^{\frac{1}{3}}} \cdot 1 : \frac{14}{3 ( x - 5 ) ^{\frac{1}{3}}}

= \frac{14}{3 ( x - 5 ) ^{\frac{1}{3}}}

\int_{\frac{1}{2}}^{7} 6 x ln (2 x) d x

\int_{- \infty}^{- 1} e^{- 2 t} d t

\frac{d}{d y} (ln (x + y))

f (x) = 2^{40}

sin (x), cos (x), [- π, π]

What is the derivative of 7(x-5)^{2/3} ?
The derivative of 7(x-5)^{2/3} is (14)/(3(x-5)^{1/3)}
What is the first derivative of 7(x-5)^{2/3} ?
The first derivative of 7(x-5)^{2/3} is (14)/(3(x-5)^{1/3)}