en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of xsqrt(6-x^2)

Solution

\frac{d}{d x} (x 6 - x^{2})

Solution

\frac{- 2 x ^{2} + 6}{6 - x ^{2}}

Solution steps

\frac{d}{d x} (x 6 - x^{2})

Apply the Product Rule:

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

f = x, g = 6 - x^{2}

= \frac{d x}{d x} 6 - x^{2} + \frac{d}{d x} (6 - x^{2}) x

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

\frac{d}{d x} (6 - x^{2}) = - \frac{x}{6 - x ^{2}}

= 1 \cdot 6 - x^{2} + (- \frac{x}{6 - x ^{2}}) x

Simplify

1 \cdot 6 - x^{2} + (- \frac{x}{6 - x ^{2}}) x : \frac{- 2 x ^{2} + 6}{6 - x ^{2}}

= \frac{- 2 x ^{2} + 6}{6 - x ^{2}}

Popular Examples

integral of-sqrt(2)sin(t)

\int - 2 sin (t) d t

sum from n=2 to infinity of 7/(2^n)

n = 2 \sum \infty \frac{7}{2 ^{n}}

integral from 0 to 1 of (32)/(x^2-64)

\int_{0}^{1} \frac{32}{x ^{2} - 64} d x

inverse oflaplace 1/(s^2*(s+1))inverse laplace

\frac{1}{s ^{2} \cdot ( s + 1 )}

derivative of f(x)= 7/2 x^{2/7}derivative of

f (x) = \frac{7}{2} x^{\frac{2}{7}}

Frequently Asked Questions (FAQ)

What is the derivative of xsqrt(6-x^2) ?
The derivative of xsqrt(6-x^2) is (-2x^2+6)/(sqrt(6-x^2))
What is the first derivative of xsqrt(6-x^2) ?
The first derivative of xsqrt(6-x^2) is (-2x^2+6)/(sqrt(6-x^2))