What is (\partial)/(\partial x)(-1/(sqrt(x^2+y^2))) ?

The answer to (\partial)/(\partial x)(-1/(sqrt(x^2+y^2))) is x/((x^2+y^2)^{3/2)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(-1/(sqrt(x^2+y^2)))

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

\frac{x}{( x ^{2} + y ^{2} ) ^{\frac{3}{2}}}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

- \frac{1}{2 ( x ^{2} + y ^{2} ) ^{\frac{3}{2}}} \frac{\partial}{\partial x} (x^{2} + y^{2})

= - \frac{1}{2 ( x ^{2} + y ^{2} ) ^{\frac{3}{2}}} \frac{\partial}{\partial x} (x^{2} + y^{2})

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

= - (- \frac{1}{2 ( x ^{2} + y ^{2} ) ^{\frac{3}{2}}} \cdot 2 x)

Simplify

- (- \frac{1}{2 ( x ^{2} + y ^{2} ) ^{\frac{3}{2}}} \cdot 2 x) : \frac{x}{( x ^{2} + y ^{2} ) ^{\frac{3}{2}}}

= \frac{x}{( x ^{2} + y ^{2} ) ^{\frac{3}{2}}}

f (x) = tan^{3} (x + csc (x))

y = 4 - x^{2}

\int 9 x^{2} - 4 x + 3 d x

What is (\partial)/(\partial x)(-1/(sqrt(x^2+y^2))) ?
The answer to (\partial)/(\partial x)(-1/(sqrt(x^2+y^2))) is x/((x^2+y^2)^{3/2)}