en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of y=sqrt(5-x^2)

Solution

derivative of

y = 5 - x^{2}

Solution

- \frac{x}{5 - x ^{2}}

Solution steps

\frac{d}{d x} (5 - x^{2})

Apply the chain rule:

\frac{1}{2 5 - x ^{2}} \frac{d}{d x} (5 - x^{2})

= \frac{1}{2 5 - x ^{2}} \frac{d}{d x} (5 - x^{2})

\frac{d}{d x} (5 - x^{2}) = - 2 x

= \frac{1}{2 5 - x ^{2}} (- 2 x)

Simplify

\frac{1}{2 5 - x ^{2}} (- 2 x) : - \frac{x}{5 - x ^{2}}

= - \frac{x}{5 - x ^{2}}

Popular Examples

integral of (6x+5)sqrt(3x^2+5x)

\int (6 x + 5) 3 x^{2} + 5 x d x

limit as t approaches 0 of (4t^2+3t+2)/(t^3+2t-6)

t \to 0 lim (\frac{4 t ^{2} + 3 t + 2}{t ^{3} + 2 t - 6})

f (x) = - x^{2} + 3 x - 1

integral of ((e^{2x}))/(e^{4x)+4}

\int \frac{( e ^{2 x} )}{e ^{4 x} + 4} d x

integral of 1/(sqrt(8-2x-x^2))

\int \frac{1}{8 - 2 x - x ^{2}} d x

Frequently Asked Questions (FAQ)

What is the derivative of y=sqrt(5-x^2) ?
The derivative of y=sqrt(5-x^2) is -x/(sqrt(5-x^2))
What is the first derivative of y=sqrt(5-x^2) ?
The first derivative of y=sqrt(5-x^2) is -x/(sqrt(5-x^2))