What is the derivative of 24x(3x^2+4)^3 ?

The derivative of 24x(3x^2+4)^3 is 24((3x^2+4)^3+18x^2(3x^2+4)^2)

What is the first derivative of 24x(3x^2+4)^3 ?

The first derivative of 24x(3x^2+4)^3 is 24((3x^2+4)^3+18x^2(3x^2+4)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

24 x (3 x^{2} + 4)^{3}

24 ((3 x^{2} + 4)^{3} + 18 x^{2} (3 x^{2} + 4)^{2})

Solution steps

\frac{d}{d x} (24 x (3 x^{2} + 4)^{3})

Take the constant out:

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

= 24 \frac{d}{d x} (x (3 x^{2} + 4)^{3})

Apply the Product Rule:

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

f = x, g = (3 x^{2} + 4)^{3}

= 24 (\frac{d x}{d x} (3 x^{2} + 4)^{3} + \frac{d}{d x} ((3 x^{2} + 4)^{3}) x)

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

\frac{d}{d x} ((3 x^{2} + 4)^{3}) = 18 x (3 x^{2} + 4)^{2}

= 24 (1 \cdot (3 x^{2} + 4)^{3} + 18 x (3 x^{2} + 4)^{2} x)

Simplify

24 (1 \cdot (3 x^{2} + 4)^{3} + 18 x (3 x^{2} + 4)^{2} x) : 24 ((3 x^{2} + 4)^{3} + 18 x^{2} (3 x^{2} + 4)^{2})

= 24 ((3 x^{2} + 4)^{3} + 18 x^{2} (3 x^{2} + 4)^{2})

\int 4 x + \frac{3}{x} d x

cos (2 t)

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

x^{2} y^{^{'}} - x = 1 + y + x y

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

What is the derivative of 24x(3x^2+4)^3 ?
The derivative of 24x(3x^2+4)^3 is 24((3x^2+4)^3+18x^2(3x^2+4)^2)
What is the first derivative of 24x(3x^2+4)^3 ?
The first derivative of 24x(3x^2+4)^3 is 24((3x^2+4)^3+18x^2(3x^2+4)^2)