What is the derivative of f(x)=(4x-5)(3x^3-x^2+1) ?

The derivative of f(x)=(4x-5)(3x^3-x^2+1) is 48x^3-57x^2+10x+4

What is the first derivative of f(x)=(4x-5)(3x^3-x^2+1) ?

The first derivative of f(x)=(4x-5)(3x^3-x^2+1) is 48x^3-57x^2+10x+4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

f (x) = (4 x - 5) (3 x^{3} - x^{2} + 1)

48 x^{3} - 57 x^{2} + 10 x + 4

Solution steps

\frac{d}{d x} ((4 x - 5) (3 x^{3} - x^{2} + 1))

Apply the Product Rule:

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

f = 4 x - 5, g = 3 x^{3} - x^{2} + 1

= \frac{d}{d x} (4 x - 5) (3 x^{3} - x^{2} + 1) + \frac{d}{d x} (3 x^{3} - x^{2} + 1) (4 x - 5)

\frac{d}{d x} (4 x - 5) = 4

\frac{d}{d x} (3 x^{3} - x^{2} + 1) = 9 x^{2} - 2 x

= 4 (3 x^{3} - x^{2} + 1) + (9 x^{2} - 2 x) (4 x - 5)

Simplify

4 (3 x^{3} - x^{2} + 1) + (9 x^{2} - 2 x) (4 x - 5) : 48 x^{3} - 57 x^{2} + 10 x + 4

= 48 x^{3} - 57 x^{2} + 10 x + 4

\int \frac{x - 3}{x ^{2} - 1} d x

x^{3}

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

x \to 1 lim (\frac{x ^{4} - 1}{x ^{2}})

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

What is the derivative of f(x)=(4x-5)(3x^3-x^2+1) ?
The derivative of f(x)=(4x-5)(3x^3-x^2+1) is 48x^3-57x^2+10x+4
What is the first derivative of f(x)=(4x-5)(3x^3-x^2+1) ?
The first derivative of f(x)=(4x-5)(3x^3-x^2+1) is 48x^3-57x^2+10x+4