What is (\partial)/(\partial x)((60)/(1+x^2+y^2)) ?

The answer to (\partial)/(\partial x)((60)/(1+x^2+y^2)) is -(120x)/((1+x^2+y^2)^2)

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(\partial)/(\partial x)((60)/(1+x^2+y^2))

\frac{\partial}{\partial x} (\frac{60}{1 + x ^{2} + y ^{2}})

- \frac{120 x}{( 1 + x ^{2} + y ^{2} ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{60}{1 + x ^{2} + y ^{2}})

Treat

y

as a constant

Take the constant out:

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

= 60 \frac{\partial}{\partial x} (\frac{1}{1 + x ^{2} + y ^{2}})

Apply exponent rule:

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

= 60 \frac{\partial}{\partial x} ((1 + x^{2} + y^{2})^{- 1})

Apply the chain rule:

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

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

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

= 60 (- \frac{1}{( 1 + x ^{2} + y ^{2} ) ^{2}} \cdot 2 x)

Simplify

60 (- \frac{1}{( 1 + x ^{2} + y ^{2} ) ^{2}} \cdot 2 x) : - \frac{120 x}{( 1 + x ^{2} + y ^{2} ) ^{2}}

= - \frac{120 x}{( 1 + x ^{2} + y ^{2} ) ^{2}}

\frac{d y}{d x} = 5 + y - 5 x + 2

x^{2} y^{^{'}} + \frac{4}{3} x y = 2 cos (3 x) y^{- \frac{1}{2}}

\frac{\partial}{\partial x} (3 x^{2} \cdot c)

t^{2} y^{^{'}} + t y = 3

\int \frac{x}{x ^{2}} d x

What is (\partial)/(\partial x)((60)/(1+x^2+y^2)) ?
The answer to (\partial)/(\partial x)((60)/(1+x^2+y^2)) is -(120x)/((1+x^2+y^2)^2)