What is the derivative of f(x)=(8x(x^2+6)^3) ?

The derivative of f(x)=(8x(x^2+6)^3) is 8((x^2+6)^3+6x^2(x^2+6)^2)

What is the first derivative of f(x)=(8x(x^2+6)^3) ?

The first derivative of f(x)=(8x(x^2+6)^3) is 8((x^2+6)^3+6x^2(x^2+6)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

f (x) = (8 x (x^{2} + 6)^{3})

8 ((x^{2} + 6)^{3} + 6 x^{2} (x^{2} + 6)^{2})

Solution steps

\frac{d}{d x} (8 x (x^{2} + 6)^{3})

Take the constant out:

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

= 8 \frac{d}{d x} (x (x^{2} + 6)^{3})

Apply the Product Rule:

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

f = x, g = (x^{2} + 6)^{3}

= 8 (\frac{d x}{d x} (x^{2} + 6)^{3} + \frac{d}{d x} ((x^{2} + 6)^{3}) x)

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

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

= 8 (1 \cdot (x^{2} + 6)^{3} + 6 x (x^{2} + 6)^{2} x)

Simplify

8 (1 \cdot (x^{2} + 6)^{3} + 6 x (x^{2} + 6)^{2} x) : 8 ((x^{2} + 6)^{3} + 6 x^{2} (x^{2} + 6)^{2})

= 8 ((x^{2} + 6)^{3} + 6 x^{2} (x^{2} + 6)^{2})

\int 3 x^{2} e^{4 x^{3}} d x

\int_{- 2}^{1} x^{2} e^{x^{3} + 8} d x

y^{^{'}} + 3 y = 1 - 6 e^{- 2 x}

\int x^{2} \cdot 6^{x^{3}} d x

x \to - 9 + lim (\frac{∣ x + 9 ∣}{x + 9})

What is the derivative of f(x)=(8x(x^2+6)^3) ?
The derivative of f(x)=(8x(x^2+6)^3) is 8((x^2+6)^3+6x^2(x^2+6)^2)
What is the first derivative of f(x)=(8x(x^2+6)^3) ?
The first derivative of f(x)=(8x(x^2+6)^3) is 8((x^2+6)^3+6x^2(x^2+6)^2)