What is the derivative of 1/((x^2+y)) ?

The derivative of 1/((x^2+y)) is -(2x)/((x^2+y)^2)

What is the first derivative of 1/((x^2+y)) ?

The first derivative of 1/((x^2+y)) is -(2x)/((x^2+y)^2)

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derivative of

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

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

Solution steps

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

Treat

y

as a constant

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

(x + y)^{3}

\frac{2}{x ^{3}} + \frac{2}{x ^{3}} - 4 x

ln (x^{2}) - 3

\frac{e ^{x}}{2} + \frac{e ^{- x}}{2}

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

What is the derivative of 1/((x^2+y)) ?
The derivative of 1/((x^2+y)) is -(2x)/((x^2+y)^2)
What is the first derivative of 1/((x^2+y)) ?
The first derivative of 1/((x^2+y)) is -(2x)/((x^2+y)^2)