What is the derivative of 1/(sqrt(2x-3)) ?

The derivative of 1/(sqrt(2x-3)) is -1/((2x-3)^{3/2)}

What is the first derivative of 1/(sqrt(2x-3)) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

5 - 4 x

e^{x^{5}}

\int sin (x^{2}) d x

\int_{0}^{\infty} e^{- 3 x} d x

\int_{0}^{\frac{π}{6}} sin (3 x) d x

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