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

The derivative of x^3(x-7^2) is 5x^4-56x^3+147x^2

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

The first derivative of x^3(x-7^2) is 5x^4-56x^3+147x^2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

5 x^{4} - 56 x^{3} + 147 x^{2}

Solution steps

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

Apply the Product Rule:

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

f = x^{3}, g = (x - 7)^{2}

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

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

\frac{d}{d x} ((x - 7)^{2}) = 2 (x - 7)

= 3 x^{2} (x - 7)^{2} + 2 (x - 7) x^{3}

Simplify

3 x^{2} (x - 7)^{2} + 2 (x - 7) x^{3} : 5 x^{4} - 56 x^{3} + 147 x^{2}

= 5 x^{4} - 56 x^{3} + 147 x^{2}

y = x^{2} - 4 x + 3, y = 3 + 4 x - x^{2}

x \to - \infty lim (e^{x})

cos (\frac{π x}{4})

\frac{d}{d x} (ln ((x - 1)^{2}))

x = 3 y, x = y^{2} - 4

What is the derivative of x^3(x-7^2) ?
The derivative of x^3(x-7^2) is 5x^4-56x^3+147x^2
What is the first derivative of x^3(x-7^2) ?
The first derivative of x^3(x-7^2) is 5x^4-56x^3+147x^2