What is (\partial)/(\partial x)((26)/((2+x^2+y^2))) ?

The answer to (\partial)/(\partial x)((26)/((2+x^2+y^2))) is -(52x)/((2+x^2+y^2)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)((26)/((2+x^2+y^2)))

\frac{\partial}{\partial x} (\frac{26}{( 2 + x ^{2} + y ^{2} )})

- \frac{52 x}{( 2 + x ^{2} + y ^{2} ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{26}{( 2 + x ^{2} + y ^{2} )})

Treat

y

as a constant

Take the constant out:

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

= 26 \frac{\partial}{\partial x} (\frac{1}{2 + x ^{2} + y ^{2}})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= 26 \frac{\partial}{\partial x} ((2 + x^{2} + y^{2})^{- 1})

Apply the chain rule:

- \frac{1}{( 2 + x ^{2} + y ^{2} ) ^{2}} \frac{\partial}{\partial x} (2 + x^{2} + y^{2})

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

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

= 26 (- \frac{1}{( 2 + x ^{2} + y ^{2} ) ^{2}} \cdot 2 x)

Simplify

26 (- \frac{1}{( 2 + x ^{2} + y ^{2} ) ^{2}} \cdot 2 x) : - \frac{52 x}{( 2 + x ^{2} + y ^{2} ) ^{2}}

= - \frac{52 x}{( 2 + x ^{2} + y ^{2} ) ^{2}}

\int e^{x} \cdot 7 x d x

(u^{2} + u) d x + u^{2} (x d u + u d x) = 0

x \to 4 lim (e^{x} + 4 x)

\int 3 2 x d x

\frac{\partial}{\partial x} (7 x sin (5 x^{2} y))

What is (\partial)/(\partial x)((26)/((2+x^2+y^2))) ?
The answer to (\partial)/(\partial x)((26)/((2+x^2+y^2))) is -(52x)/((2+x^2+y^2)^2)