What is the derivative of f(x)=(3x-2)(4x^3-x^2+1) ?

The derivative of f(x)=(3x-2)(4x^3-x^2+1) is 48x^3-33x^2+4x+3

What is the first derivative of f(x)=(3x-2)(4x^3-x^2+1) ?

The first derivative of f(x)=(3x-2)(4x^3-x^2+1) is 48x^3-33x^2+4x+3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

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

48 x^{3} - 33 x^{2} + 4 x + 3

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} (4 x^{3} - x^{2} + 1) = 12 x^{2} - 2 x

= 3 (4 x^{3} - x^{2} + 1) + (12 x^{2} - 2 x) (3 x - 2)

Simplify

3 (4 x^{3} - x^{2} + 1) + (12 x^{2} - 2 x) (3 x - 2) : 48 x^{3} - 33 x^{2} + 4 x + 3

= 48 x^{3} - 33 x^{2} + 4 x + 3

\frac{d}{d x} (6 x e^{x^{2}})

x \to 2 lim (x^{2} - 6 x + 3)

\frac{d}{d x} (\frac{1}{1 + e ^{0.5 x}})

n = 1 \sum \infty n e^{- 6 n}

\frac{d ^{2}}{d z ^{2}} (z^{2} e^{z})

What is the derivative of f(x)=(3x-2)(4x^3-x^2+1) ?
The derivative of f(x)=(3x-2)(4x^3-x^2+1) is 48x^3-33x^2+4x+3
What is the first derivative of f(x)=(3x-2)(4x^3-x^2+1) ?
The first derivative of f(x)=(3x-2)(4x^3-x^2+1) is 48x^3-33x^2+4x+3