What is the derivative of 48x(4x^2+9)^5 ?

The derivative of 48x(4x^2+9)^5 is 48((4x^2+9)^5+40x^2(4x^2+9)^4)

What is the first derivative of 48x(4x^2+9)^5 ?

The first derivative of 48x(4x^2+9)^5 is 48((4x^2+9)^5+40x^2(4x^2+9)^4)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

48 x (4 x^{2} + 9)^{5}

48 ((4 x^{2} + 9)^{5} + 40 x^{2} (4 x^{2} + 9)^{4})

Solution steps

\frac{d}{d x} (48 x (4 x^{2} + 9)^{5})

Take the constant out:

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

= 48 \frac{d}{d x} (x (4 x^{2} + 9)^{5})

Apply the Product Rule:

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

f = x, g = (4 x^{2} + 9)^{5}

= 48 (\frac{d x}{d x} (4 x^{2} + 9)^{5} + \frac{d}{d x} ((4 x^{2} + 9)^{5}) x)

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

\frac{d}{d x} ((4 x^{2} + 9)^{5}) = 40 x (4 x^{2} + 9)^{4}

= 48 (1 \cdot (4 x^{2} + 9)^{5} + 40 x (4 x^{2} + 9)^{4} x)

Simplify

48 (1 \cdot (4 x^{2} + 9)^{5} + 40 x (4 x^{2} + 9)^{4} x) : 48 ((4 x^{2} + 9)^{5} + 40 x^{2} (4 x^{2} + 9)^{4})

= 48 ((4 x^{2} + 9)^{5} + 40 x^{2} (4 x^{2} + 9)^{4})

What is the derivative of 48x(4x^2+9)^5 ?
The derivative of 48x(4x^2+9)^5 is 48((4x^2+9)^5+40x^2(4x^2+9)^4)
What is the first derivative of 48x(4x^2+9)^5 ?
The first derivative of 48x(4x^2+9)^5 is 48((4x^2+9)^5+40x^2(4x^2+9)^4)