en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

derivative of y=x^3(3-x^2)

Solution

derivative of

y = x^{3} (3 - x^{2})

Solution

9 x^{2} - 5 x^{4}

Solution steps

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

Apply the Product Rule:

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

f = x^{3}, g = 3 - x^{2}

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

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

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

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

Simplify

3 x^{2} (3 - x^{2}) + (- 2 x) x^{3} : 9 x^{2} - 5 x^{4}

= 9 x^{2} - 5 x^{4}

Graph

Popular Examples

(\partial)/(\partial x)(sin(pi(4x-2y)))

\frac{\partial}{\partial x} (sin (π (4 x - 2 y)))

slope of y=3x^2,\at x=1

s l o p e y = 3 x^{2}, at x = 1

integral of (sec^5(x))

\int (sec^{5} (x)) d x

slope ofintercept (-4,5),(5,-22)

s l o p e in t erce pt (- 4, 5), (5, - 22)

limit as x approaches 6 of pi

x \to 6 lim (π)

Frequently Asked Questions (FAQ)

What is the derivative of y=x^3(3-x^2) ?
The derivative of y=x^3(3-x^2) is 9x^2-5x^4
What is the first derivative of y=x^3(3-x^2) ?
The first derivative of y=x^3(3-x^2) is 9x^2-5x^4