What is the derivative of (2x-1(sqrt(3-4x))) ?

The derivative of (2x-1(sqrt(3-4x))) is (-12x+8)/(sqrt(3-4x))

What is the first derivative of (2x-1(sqrt(3-4x))) ?

The first derivative of (2x-1(sqrt(3-4x))) is (-12x+8)/(sqrt(3-4x))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

\frac{- 12 x + 8}{3 - 4 x}

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 2 x - 1, g = 3 - 4 x

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

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

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

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

Simplify

2 3 - 4 x + (- \frac{2}{3 - 4 x}) (2 x - 1) : \frac{- 12 x + 8}{3 - 4 x}

= \frac{- 12 x + 8}{3 - 4 x}

What is the derivative of (2x-1(sqrt(3-4x))) ?
The derivative of (2x-1(sqrt(3-4x))) is (-12x+8)/(sqrt(3-4x))
What is the first derivative of (2x-1(sqrt(3-4x))) ?
The first derivative of (2x-1(sqrt(3-4x))) is (-12x+8)/(sqrt(3-4x))