What is (\partial)/(\partial x)((53)/(5+x^2+y^2)) ?

The answer to (\partial)/(\partial x)((53)/(5+x^2+y^2)) is -(106x)/((5+x^2+y^2)^2)

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(\partial)/(\partial x)((53)/(5+x^2+y^2))

\frac{\partial}{\partial x} (\frac{53}{5 + x ^{2} + y ^{2}})

- \frac{106 x}{( 5 + x ^{2} + y ^{2} ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{53}{5 + x ^{2} + y ^{2}})

Treat

y

as a constant

Take the constant out:

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

= 53 \frac{\partial}{\partial x} (\frac{1}{5 + x ^{2} + y ^{2}})

Apply exponent rule:

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

= 53 \frac{\partial}{\partial x} ((5 + x^{2} + y^{2})^{- 1})

Apply the chain rule:

- \frac{1}{( 5 + x ^{2} + y ^{2} ) ^{2}} \frac{\partial}{\partial x} (5 + x^{2} + y^{2})

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

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

= 53 (- \frac{1}{( 5 + x ^{2} + y ^{2} ) ^{2}} \cdot 2 x)

Simplify

53 (- \frac{1}{( 5 + x ^{2} + y ^{2} ) ^{2}} \cdot 2 x) : - \frac{106 x}{( 5 + x ^{2} + y ^{2} ) ^{2}}

= - \frac{106 x}{( 5 + x ^{2} + y ^{2} ) ^{2}}

x \to 1 lim (sin (2 x))

\frac{d}{d x} (5 sin (π x))

\frac{d}{d x} (\frac{x ^{3}}{3} - 4 x + 1)

y^{^{''}} - y^{^{'}} + \frac{1}{4} y = 3 + e^{\frac{x}{2}}

\frac{d}{d x} (4 x^{3} + 2)

What is (\partial)/(\partial x)((53)/(5+x^2+y^2)) ?
The answer to (\partial)/(\partial x)((53)/(5+x^2+y^2)) is -(106x)/((5+x^2+y^2)^2)