en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of 8(x^3-x^4)

Solution

\frac{d}{d x} (8 (x^{3} - x)^{4})

Solution

32 (x^{3} - x)^{3} (3 x^{2} - 1)

Solution steps

\frac{d}{d x} (8 (x^{3} - x)^{4})

Take the constant out:

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

= 8 \frac{d}{d x} ((x^{3} - x)^{4})

Apply the chain rule:

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

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

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

= 8 \cdot 4 (x^{3} - x)^{3} (3 x^{2} - 1)

Simplify

= 32 (x^{3} - x)^{3} (3 x^{2} - 1)

Popular Examples

derivative of f(x)=1.58e^{-0.213x}derivative of

f (x) = 1.58 e^{- 0.213 x}

derivative of f(x)=(4x)/(e^x)derivative of

f (x) = \frac{4 x}{e ^{x}}

derivative of sqrt(35x)ln(20x)derivative of

35 x ln (20 x)

integral of (15x^{-2}-5x)cos(6x^{-1}+x^2)

\int (15 x^{- 2} - 5 x) cos (6 x^{- 1} + x^{2}) d x

integral of 2^s

\int 2^{s} d s

Frequently Asked Questions (FAQ)

What is the derivative of 8(x^3-x^4) ?
The derivative of 8(x^3-x^4) is 32(x^3-x)^3(3x^2-1)
What is the first derivative of 8(x^3-x^4) ?
The first derivative of 8(x^3-x^4) is 32(x^3-x)^3(3x^2-1)