What is (\partial)/(\partial x)((61)/(7+x^2+y^2)) ?

The answer to (\partial)/(\partial x)((61)/(7+x^2+y^2)) is -(122x)/((7+x^2+y^2)^2)

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(\partial)/(\partial x)((61)/(7+x^2+y^2))

\frac{\partial}{\partial x} (\frac{61}{7 + x ^{2} + y ^{2}})

- \frac{122 x}{( 7 + x ^{2} + y ^{2} ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{61}{7 + x ^{2} + y ^{2}})

Treat

y

as a constant

Take the constant out:

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

= 61 \frac{\partial}{\partial x} (\frac{1}{7 + x ^{2} + y ^{2}})

Apply exponent rule:

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

= 61 \frac{\partial}{\partial x} ((7 + x^{2} + y^{2})^{- 1})

Apply the chain rule:

- \frac{1}{( 7 + x ^{2} + y ^{2} ) ^{2}} \frac{\partial}{\partial x} (7 + x^{2} + y^{2})

= - \frac{1}{( 7 + x ^{2} + y ^{2} ) ^{2}} \frac{\partial}{\partial x} (7 + x^{2} + y^{2})

\frac{\partial}{\partial x} (7 + x^{2} + y^{2}) = 2 x

= 61 (- \frac{1}{( 7 + x ^{2} + y ^{2} ) ^{2}} \cdot 2 x)

Simplify

61 (- \frac{1}{( 7 + x ^{2} + y ^{2} ) ^{2}} \cdot 2 x) : - \frac{122 x}{( 7 + x ^{2} + y ^{2} ) ^{2}}

= - \frac{122 x}{( 7 + x ^{2} + y ^{2} ) ^{2}}

x \to 3 lim (\frac{x ^{2} + 1}{x - 3})

\frac{d}{d x} (sin (x^{2} + 5))

\frac{d}{d x} (\frac{7 x}{e ^{x}})

n = 1 \sum \infty \frac{9}{1 0 ^{n}}

\frac{d}{d t} (cos (3 t))

What is (\partial)/(\partial x)((61)/(7+x^2+y^2)) ?
The answer to (\partial)/(\partial x)((61)/(7+x^2+y^2)) is -(122x)/((7+x^2+y^2)^2)