What is the derivative of 6x(x^2-1)^2 ?

The derivative of 6x(x^2-1)^2 is 6(5x^4-6x^2+1)

What is the first derivative of 6x(x^2-1)^2 ?

The first derivative of 6x(x^2-1)^2 is 6(5x^4-6x^2+1)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

6 x (x^{2} - 1)^{2}

6 (5 x^{4} - 6 x^{2} + 1)

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x, g = (x^{2} - 1)^{2}

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

\frac{d x}{d x} = 1

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

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

Simplify

6 (1 \cdot (x^{2} - 1)^{2} + 4 x (x^{2} - 1) x) : 6 (5 x^{4} - 6 x^{2} + 1)

= 6 (5 x^{4} - 6 x^{2} + 1)

\int x^{3} 0. 2^{- x} x d x

x \to + (- 2) lim (\frac{8}{x})

9 x ln (1 + 2 x)

y^{(\frac{1}{2})} \frac{d y}{d x} + y^{(\frac{3}{2})} = 1, y (0) = 4

\frac{d}{d x} (ln (x + y^{2}))

What is the derivative of 6x(x^2-1)^2 ?
The derivative of 6x(x^2-1)^2 is 6(5x^4-6x^2+1)
What is the first derivative of 6x(x^2-1)^2 ?
The first derivative of 6x(x^2-1)^2 is 6(5x^4-6x^2+1)