What is (\partial)/(\partial x)((55)/((9+x^2+y^2))) ?

The answer to (\partial)/(\partial x)((55)/((9+x^2+y^2))) is -(110x)/((9+x^2+y^2)^2)

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(\partial)/(\partial x)((55)/((9+x^2+y^2)))

\frac{\partial}{\partial x} (\frac{55}{( 9 + x ^{2} + y ^{2} )})

- \frac{110 x}{( 9 + x ^{2} + y ^{2} ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{55}{( 9 + x ^{2} + y ^{2} )})

Treat

y

as a constant

Take the constant out:

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

= 55 \frac{\partial}{\partial x} (\frac{1}{9 + x ^{2} + y ^{2}})

Apply exponent rule:

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

= 55 \frac{\partial}{\partial x} ((9 + x^{2} + y^{2})^{- 1})

Apply the chain rule:

- \frac{1}{( 9 + x ^{2} + y ^{2} ) ^{2}} \frac{\partial}{\partial x} (9 + x^{2} + y^{2})

= - \frac{1}{( 9 + x ^{2} + y ^{2} ) ^{2}} \frac{\partial}{\partial x} (9 + x^{2} + y^{2})

\frac{\partial}{\partial x} (9 + x^{2} + y^{2}) = 2 x

= 55 (- \frac{1}{( 9 + x ^{2} + y ^{2} ) ^{2}} \cdot 2 x)

Simplify

55 (- \frac{1}{( 9 + x ^{2} + y ^{2} ) ^{2}} \cdot 2 x) : - \frac{110 x}{( 9 + x ^{2} + y ^{2} ) ^{2}}

= - \frac{110 x}{( 9 + x ^{2} + y ^{2} ) ^{2}}

y^{^{'}} + \frac{3}{4} y = 1 - \frac{t}{3}

e^{l n (1 + \frac{1}{k})}

\int_{0}^{2 π} t^{2} sin (2 t) d t

f (x) = \frac{32}{x ^{3}}

x + 2, 1, 3

What is (\partial)/(\partial x)((55)/((9+x^2+y^2))) ?
The answer to (\partial)/(\partial x)((55)/((9+x^2+y^2))) is -(110x)/((9+x^2+y^2)^2)