What is (\partial)/(\partial x)((2x)/(x^2+y-5)) ?

The answer to (\partial)/(\partial x)((2x)/(x^2+y-5)) is (2(-x^2+y-5))/((x^2+y-5)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)((2x)/(x^2+y-5))

\frac{\partial}{\partial x} (\frac{2 x}{x ^{2} + y - 5})

\frac{2 ( - x ^{2} + y - 5 )}{( x ^{2} + y - 5 ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{2 x}{x ^{2} + y - 5})

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{\partial}{\partial x} (\frac{x}{x ^{2} + y - 5})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= 2 \cdot \frac{\frac{\partial}{\partial x} ( x ) ( x ^{2} + y - 5 ) - \frac{\partial}{\partial x} ( x ^{2} + y - 5 ) x}{( x ^{2} + y - 5 ) ^{2}}

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (x^{2} + y - 5) = 2 x

= 2 \cdot \frac{1 \cdot ( x ^{2} + y - 5 ) - 2 xx}{( x ^{2} + y - 5 ) ^{2}}

Simplify

2 \cdot \frac{1 \cdot ( x ^{2} + y - 5 ) - 2 xx}{( x ^{2} + y - 5 ) ^{2}} : \frac{2 ( - x ^{2} + y - 5 )}{( x ^{2} + y - 5 ) ^{2}}

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

\frac{d y}{d x} = b \cdot (1 - y) \cdot y

\int_{0}^{\frac{π}{3}} sin^{2} (x) d x

\int_{0}^{1} \frac{1}{x ^{0}} d x

y^{2} - 5 x = 4, x - y = 2

x^{\frac{1}{2}}

What is (\partial)/(\partial x)((2x)/(x^2+y-5)) ?
The answer to (\partial)/(\partial x)((2x)/(x^2+y-5)) is (2(-x^2+y-5))/((x^2+y-5)^2)