What is (\partial)/(\partial x)(1/(x+y^2)) ?

The answer to (\partial)/(\partial x)(1/(x+y^2)) is -1/((x+y^2)^2)

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(\partial)/(\partial x)(1/(x+y^2))

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

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

Solution steps

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

Treat

y

as a constant

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int (x + 1) 5^{(x + 1)^{2}} d x

\frac{d}{d x} (e^{x} - 3 x^{2})

\frac{d}{d x} (25 + x^{2})

x y^{2} - y^{^{'}} x^{2} = 0

What is (\partial)/(\partial x)(1/(x+y^2)) ?
The answer to (\partial)/(\partial x)(1/(x+y^2)) is -1/((x+y^2)^2)