What is the derivative of y=(2/((2x-6) 3/2)) ?

The derivative of y=(2/((2x-6) 3/2)) is -2/(3(x-3)^2)

What is the first derivative of y=(2/((2x-6) 3/2)) ?

The first derivative of y=(2/((2x-6) 3/2)) is -2/(3(x-3)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

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

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

Solution steps

\frac{d}{d x} (\frac{2}{( 2 x - 6 ) \frac{3}{2}})

Take the constant out:

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

= \frac{2}{\frac{3}{2}} \frac{d}{d x} (\frac{1}{2 x - 6})

Apply exponent rule:

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

= \frac{2}{\frac{3}{2}} \frac{d}{d x} ((2 x - 6)^{- 1})

Apply the chain rule:

- \frac{1}{( 2 x - 6 ) ^{2}} \frac{d}{d x} (2 x - 6)

= - \frac{1}{( 2 x - 6 ) ^{2}} \frac{d}{d x} (2 x - 6)

\frac{d}{d x} (2 x - 6) = 2

= \frac{2}{\frac{3}{2}} (- \frac{1}{( 2 x - 6 ) ^{2}} \cdot 2)

Simplify

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

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

- sin (\frac{x}{2})

x \to - 1 lim (10 x (14 x - 3))

\int \frac{( arctan ( x ) ) ^{5}}{1 + x ^{2}} d x

\int \frac{x ^{4} + 1}{x ^{3} + x ^{2}} d x

\frac{\partial}{\partial y} (tan (1 + 2 x^{2} y^{4} z^{2}))

What is the derivative of y=(2/((2x-6) 3/2)) ?
The derivative of y=(2/((2x-6) 3/2)) is -2/(3(x-3)^2)
What is the first derivative of y=(2/((2x-6) 3/2)) ?
The first derivative of y=(2/((2x-6) 3/2)) is -2/(3(x-3)^2)