What is the derivative of y=x^3(x^2+5)^3 ?

The derivative of y=x^3(x^2+5)^3 is 3x^2(x^2+5)^3+6x^4(x^2+5)^2

What is the first derivative of y=x^3(x^2+5)^3 ?

The first derivative of y=x^3(x^2+5)^3 is 3x^2(x^2+5)^3+6x^4(x^2+5)^2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

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

3 x^{2} (x^{2} + 5)^{3} + 6 x^{4} (x^{2} + 5)^{2}

Solution steps

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

Apply the Product Rule:

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

f = x^{3}, g = (x^{2} + 5)^{3}

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

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

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

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

6 x (x^{2} + 5)^{2} x^{3} = 6 x^{4} (x^{2} + 5)^{2}

= 3 x^{2} (x^{2} + 5)^{3} + 6 x^{4} (x^{2} + 5)^{2}

(1 - a)^{n}

ln (\frac{x}{3})

\frac{5}{x \cdot 1}

\frac{d}{d p} (140 p^{\frac{1}{3}})

\frac{d}{dd} (n (1 - d \cdot n))

What is the derivative of y=x^3(x^2+5)^3 ?
The derivative of y=x^3(x^2+5)^3 is 3x^2(x^2+5)^3+6x^4(x^2+5)^2
What is the first derivative of y=x^3(x^2+5)^3 ?
The first derivative of y=x^3(x^2+5)^3 is 3x^2(x^2+5)^3+6x^4(x^2+5)^2