What is the derivative of x^2(x+sin(x)^5) ?

The derivative of x^2(x+sin(x)^5) is 2x(x+sin(x))^5+5(x+sin(x))^4(1+cos(x))x^2

What is the first derivative of x^2(x+sin(x)^5) ?

The first derivative of x^2(x+sin(x)^5) is 2x(x+sin(x))^5+5(x+sin(x))^4(1+cos(x))x^2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (x^{2} (x + sin (x))^{5})

2 x (x + sin (x))^{5} + 5 (x + sin (x))^{4} (1 + cos (x)) x^{2}

Solution steps

\frac{d}{d x} (x^{2} (x + sin (x))^{5})

Apply the Product Rule:

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

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

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

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} ((x + sin (x))^{5}) = 5 (x + sin (x))^{4} (1 + cos (x))

= 2 x (x + sin (x))^{5} + 5 (x + sin (x))^{4} (1 + cos (x)) x^{2}

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