en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of (2x-4(-3x^2+1))

Solution

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

Solution

- 18 x^{2} + 24 x + 2

Solution steps

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

Apply the Product Rule:

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

f = 2 x - 4, g = - 3 x^{2} + 1

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

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

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

= 2 (- 3 x^{2} + 1) + (- 6 x) (2 x - 4)

Simplify

2 (- 3 x^{2} + 1) + (- 6 x) (2 x - 4) : - 18 x^{2} + 24 x + 2

= - 18 x^{2} + 24 x + 2

Popular Examples

limit as x approaches-5 of (5-|x|)/(5+x)

x \to - 5 lim (\frac{5 - ∣ x ∣}{5 + x})

integral of tan^{15}(x)sec^4(x)

\int tan^{15} (x) sec^{4} (x) d x

integral of 1/(x^2sqrt(4x+1))

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

derivative of-e^{-x}+1

\frac{d}{d x} (- e^{- x} + 1)

integral from-2 to-1 of (x-1/(x^2))

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

Frequently Asked Questions (FAQ)

What is the derivative of (2x-4(-3x^2+1)) ?
The derivative of (2x-4(-3x^2+1)) is -18x^2+24x+2
What is the first derivative of (2x-4(-3x^2+1)) ?
The first derivative of (2x-4(-3x^2+1)) is -18x^2+24x+2