What is the derivative of-4/((4x-17)^{3/2)} ?

The derivative of-4/((4x-17)^{3/2)} is (24)/((4x-17)^{5/2)}

What is the first derivative of-4/((4x-17)^{3/2)} ?

The first derivative of-4/((4x-17)^{3/2)} is (24)/((4x-17)^{5/2)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

- \frac{4}{( 4 x - 17 ) ^{\frac{3}{2}}}

\frac{24}{( 4 x - 17 ) ^{\frac{5}{2}}}

Solution steps

\frac{d}{d x} (- \frac{4}{( 4 x - 17 ) ^{\frac{3}{2}}})

Take the constant out:

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

= - 4 \frac{d}{d x} (\frac{1}{( 4 x - 17 ) ^{\frac{3}{2}}})

Apply exponent rule:

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

= - 4 \frac{d}{d x} ((4 x - 17)^{- \frac{3}{2}})

Apply the chain rule:

- \frac{3}{2 ( 4 x - 17 ) ^{\frac{5}{2}}} \frac{d}{d x} (4 x - 17)

= - \frac{3}{2 ( 4 x - 17 ) ^{\frac{5}{2}}} \frac{d}{d x} (4 x - 17)

\frac{d}{d x} (4 x - 17) = 4

= - 4 (- \frac{3}{2 ( 4 x - 17 ) ^{\frac{5}{2}}} \cdot 4)

Simplify

- 4 (- \frac{3}{2 ( 4 x - 17 ) ^{\frac{5}{2}}} \cdot 4) : \frac{24}{( 4 x - 17 ) ^{\frac{5}{2}}}

= \frac{24}{( 4 x - 17 ) ^{\frac{5}{2}}}

What is the derivative of-4/((4x-17)^{3/2)} ?
The derivative of-4/((4x-17)^{3/2)} is (24)/((4x-17)^{5/2)}
What is the first derivative of-4/((4x-17)^{3/2)} ?
The first derivative of-4/((4x-17)^{3/2)} is (24)/((4x-17)^{5/2)}