What is (\partial)/(\partial y)(1/(x^3-y^2)) ?

The answer to (\partial)/(\partial y)(1/(x^3-y^2)) is (2y)/((x^3-y^2)^2)

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(\partial)/(\partial y)(1/(x^3-y^2))

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

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

Solution steps

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

Treat

x

as a constant

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

f (x) = x^{2} + 3, at x = 1

x \to - 10 - lim (\frac{x + 9}{x + 10})

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

\int \frac{sin ( 2 x )}{37 + cos ^{2} ( x )} d x

\int x \cdot lo g_{10} (x) d x

What is (\partial)/(\partial y)(1/(x^3-y^2)) ?
The answer to (\partial)/(\partial y)(1/(x^3-y^2)) is (2y)/((x^3-y^2)^2)