What is (\partial)/(\partial x)((200)/((x^2+y^2))) ?

The answer to (\partial)/(\partial x)((200)/((x^2+y^2))) is -(400x)/((x^2+y^2)^2)

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(\partial)/(\partial x)((200)/((x^2+y^2)))

\frac{\partial}{\partial x} (\frac{200}{( x ^{2} + y ^{2} )})

- \frac{400 x}{( x ^{2} + y ^{2} ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{200}{( x ^{2} + y ^{2} )})

Treat

y

as a constant

Take the constant out:

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

= 200 \frac{\partial}{\partial x} (\frac{1}{x ^{2} + y ^{2}})

Apply exponent rule:

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

= 200 \frac{\partial}{\partial x} ((x^{2} + y^{2})^{- 1})

Apply the chain rule:

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

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

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

= 200 (- \frac{1}{( x ^{2} + y ^{2} ) ^{2}} \cdot 2 x)

Simplify

200 (- \frac{1}{( x ^{2} + y ^{2} ) ^{2}} \cdot 2 x) : - \frac{400 x}{( x ^{2} + y ^{2} ) ^{2}}

= - \frac{400 x}{( x ^{2} + y ^{2} ) ^{2}}

\frac{2}{2 s + 1}

x \to 0 lim ((1 + 4 x) \frac{1}{x})

f (x) = x^{4}, at x = 4

x \to \infty lim (\frac{ln ( x ) + x}{x n x})

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

What is (\partial)/(\partial x)((200)/((x^2+y^2))) ?
The answer to (\partial)/(\partial x)((200)/((x^2+y^2))) is -(400x)/((x^2+y^2)^2)