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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

x 2 - x^{2}

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

e^{- 3 t} sin (4 t)

\int \frac{1}{y ( y ^{2} + 1 )} d y

\int \frac{25 - 4 x ^{2}}{x} d x

\int_{2}^{\infty} \frac{1}{x ^{2} + 4} d x

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