What is the derivative of xsqrt(a^2-x^2) ?

The derivative of xsqrt(a^2-x^2) is (-2x^2+a^2)/(sqrt(a^2-x^2))

What is the first derivative of xsqrt(a^2-x^2) ?

The first derivative of xsqrt(a^2-x^2) is (-2x^2+a^2)/(sqrt(a^2-x^2))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

\frac{- 2 x ^{2} + a ^{2}}{a ^{2} - x ^{2}}

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

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

= 1 \cdot a^{2} - x^{2} + (- \frac{x}{a ^{2} - x ^{2}}) x

Simplify

1 \cdot a^{2} - x^{2} + (- \frac{x}{a ^{2} - x ^{2}}) x : \frac{- 2 x ^{2} + a ^{2}}{a ^{2} - x ^{2}}

= \frac{- 2 x ^{2} + a ^{2}}{a ^{2} - x ^{2}}

What is the derivative of xsqrt(a^2-x^2) ?
The derivative of xsqrt(a^2-x^2) is (-2x^2+a^2)/(sqrt(a^2-x^2))
What is the first derivative of xsqrt(a^2-x^2) ?
The first derivative of xsqrt(a^2-x^2) is (-2x^2+a^2)/(sqrt(a^2-x^2))