What is the derivative of 7(x^2+3x)^6(2x+3) ?

The derivative of 7(x^2+3x)^6(2x+3) is 7(6(x^2+3x)^5(2x+3)^2+2(x^2+3x)^6)

What is the first derivative of 7(x^2+3x)^6(2x+3) ?

The first derivative of 7(x^2+3x)^6(2x+3) is 7(6(x^2+3x)^5(2x+3)^2+2(x^2+3x)^6)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

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

7 (6 (x^{2} + 3 x)^{5} (2 x + 3)^{2} + 2 (x^{2} + 3 x)^{6})

Solution steps

\frac{d}{d x} (7 (x^{2} + 3 x)^{6} (2 x + 3))

Take the constant out:

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

= 7 \frac{d}{d x} ((x^{2} + 3 x)^{6} (2 x + 3))

Apply the Product Rule:

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

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

= 7 (\frac{d}{d x} ((x^{2} + 3 x)^{6}) (2 x + 3) + \frac{d}{d x} (2 x + 3) (x^{2} + 3 x)^{6})

\frac{d}{d x} ((x^{2} + 3 x)^{6}) = 6 (x^{2} + 3 x)^{5} (2 x + 3)

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

= 7 (6 (x^{2} + 3 x)^{5} (2 x + 3) (2 x + 3) + 2 (x^{2} + 3 x)^{6})

6 (x^{2} + 3 x)^{5} (2 x + 3) (2 x + 3) = 6 (x^{2} + 3 x)^{5} (2 x + 3)^{2}

= 7 (6 (x^{2} + 3 x)^{5} (2 x + 3)^{2} + 2 (x^{2} + 3 x)^{6})

What is the derivative of 7(x^2+3x)^6(2x+3) ?
The derivative of 7(x^2+3x)^6(2x+3) is 7(6(x^2+3x)^5(2x+3)^2+2(x^2+3x)^6)
What is the first derivative of 7(x^2+3x)^6(2x+3) ?
The first derivative of 7(x^2+3x)^6(2x+3) is 7(6(x^2+3x)^5(2x+3)^2+2(x^2+3x)^6)