What is the derivative of f(x)=x^2sqrt(9-x^2) ?

The derivative of f(x)=x^2sqrt(9-x^2) is (-3x^3+18x)/(sqrt(9-x^2))

What is the first derivative of f(x)=x^2sqrt(9-x^2) ?

The first derivative of f(x)=x^2sqrt(9-x^2) is (-3x^3+18x)/(sqrt(9-x^2))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

f (x) = x^{2} 9 - x^{2}

\frac{- 3 x ^{3} + 18 x}{9 - x ^{2}}

Solution steps

\frac{d}{d x} (x^{2} 9 - x^{2})

Apply the Product Rule:

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

f = x^{2}, g = 9 - x^{2}

= \frac{d}{d x} (x^{2}) 9 - x^{2} + \frac{d}{d x} (9 - x^{2}) x^{2}

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

\frac{d}{d x} (9 - x^{2}) = - \frac{x}{9 - x ^{2}}

= 2 x 9 - x^{2} + (- \frac{x}{9 - x ^{2}}) x^{2}

Simplify

2 x 9 - x^{2} + (- \frac{x}{9 - x ^{2}}) x^{2} : \frac{- 3 x ^{3} + 18 x}{9 - x ^{2}}

= \frac{- 3 x ^{3} + 18 x}{9 - x ^{2}}

What is the derivative of f(x)=x^2sqrt(9-x^2) ?
The derivative of f(x)=x^2sqrt(9-x^2) is (-3x^3+18x)/(sqrt(9-x^2))
What is the first derivative of f(x)=x^2sqrt(9-x^2) ?
The first derivative of f(x)=x^2sqrt(9-x^2) is (-3x^3+18x)/(sqrt(9-x^2))