What is the derivative of x^4(7-x^2^3) ?

The derivative of x^4(7-x^2^3) is 4x^3(7-x^2)^3-6x^5(7-x^2)^2

What is the first derivative of x^4(7-x^2^3) ?

The first derivative of x^4(7-x^2^3) is 4x^3(7-x^2)^3-6x^5(7-x^2)^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^{4} (7 - x^{2})^{3})

4 x^{3} (7 - x^{2})^{3} - 6 x^{5} (7 - x^{2})^{2}

Solution steps

\frac{d}{d x} (x^{4} (7 - x^{2})^{3})

Apply the Product Rule:

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

f = x^{4}, g = (7 - x^{2})^{3}

= \frac{d}{d x} (x^{4}) (7 - x^{2})^{3} + \frac{d}{d x} ((7 - x^{2})^{3}) x^{4}

\frac{d}{d x} (x^{4}) = 4 x^{3}

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

= 4 x^{3} (7 - x^{2})^{3} + (- 6 x (7 - x^{2})^{2}) x^{4}

Simplify

4 x^{3} (7 - x^{2})^{3} + (- 6 x (7 - x^{2})^{2}) x^{4} : 4 x^{3} (7 - x^{2})^{3} - 6 x^{5} (7 - x^{2})^{2}

= 4 x^{3} (7 - x^{2})^{3} - 6 x^{5} (7 - x^{2})^{2}

\int arctan (tan (x)) d x

\int \frac{45}{1 - cos ( 5 x )} d x

- 4

f (- 1) = - x^{3}

f (x) = x^{3} - 3 x + 1, (4, 53)

What is the derivative of x^4(7-x^2^3) ?
The derivative of x^4(7-x^2^3) is 4x^3(7-x^2)^3-6x^5(7-x^2)^2
What is the first derivative of x^4(7-x^2^3) ?
The first derivative of x^4(7-x^2^3) is 4x^3(7-x^2)^3-6x^5(7-x^2)^2