What is (\partial)/(\partial x)((100)/(x^2+y^2+3)) ?

The answer to (\partial)/(\partial x)((100)/(x^2+y^2+3)) is -(200x)/((x^2+y^2+3)^2)

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(\partial)/(\partial x)((100)/(x^2+y^2+3))

\frac{\partial}{\partial x} (\frac{100}{x ^{2} + y ^{2} + 3})

- \frac{200 x}{( x ^{2} + y ^{2} + 3 ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{100}{x ^{2} + y ^{2} + 3})

Treat

y

as a constant

Take the constant out:

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

= 100 \frac{\partial}{\partial x} (\frac{1}{x ^{2} + y ^{2} + 3})

Apply exponent rule:

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

= 100 \frac{\partial}{\partial x} ((x^{2} + y^{2} + 3)^{- 1})

Apply the chain rule:

- \frac{1}{( x ^{2} + y ^{2} + 3 ) ^{2}} \frac{\partial}{\partial x} (x^{2} + y^{2} + 3)

= - \frac{1}{( x ^{2} + y ^{2} + 3 ) ^{2}} \frac{\partial}{\partial x} (x^{2} + y^{2} + 3)

\frac{\partial}{\partial x} (x^{2} + y^{2} + 3) = 2 x

= 100 (- \frac{1}{( x ^{2} + y ^{2} + 3 ) ^{2}} \cdot 2 x)

Simplify

100 (- \frac{1}{( x ^{2} + y ^{2} + 3 ) ^{2}} \cdot 2 x) : - \frac{200 x}{( x ^{2} + y ^{2} + 3 ) ^{2}}

= - \frac{200 x}{( x ^{2} + y ^{2} + 3 ) ^{2}}

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

n = 0 \sum \infty \frac{ln ( n )}{n}

(\frac{16}{x ( 4 - x ^{2} )})^{^{'}}

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What is (\partial)/(\partial x)((100)/(x^2+y^2+3)) ?
The answer to (\partial)/(\partial x)((100)/(x^2+y^2+3)) is -(200x)/((x^2+y^2+3)^2)