What is (\partial)/(\partial x)((e^x-2y^{-3})^{2/5}) ?

The answer to (\partial)/(\partial x)((e^x-2y^{-3})^{2/5}) is (2e^xy^{9/5})/(5(e^xy^3-2)^{3/5)}

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(\partial)/(\partial x)((e^x-2y^{-3})^{2/5})

\frac{\partial}{\partial x} ((e^{x} - 2 y^{- 3})^{\frac{2}{5}})

\frac{2 e ^{x} y ^{\frac{9}{5}}}{5 ( e ^{x} y ^{3} - 2 ) ^{\frac{3}{5}}}

Solution steps

\frac{\partial}{\partial x} ((e^{x} - 2 y^{- 3})^{\frac{2}{5}})

Treat

y

as a constant

Apply the chain rule:

\frac{2}{5 ( e ^{x} - 2 y ^{- 3} ) ^{\frac{3}{5}}} \frac{\partial}{\partial x} (e^{x} - 2 y^{- 3})

= \frac{2}{5 ( e ^{x} - 2 y ^{- 3} ) ^{\frac{3}{5}}} \frac{\partial}{\partial x} (e^{x} - 2 y^{- 3})

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

= \frac{2}{5 ( e ^{x} - 2 y ^{- 3} ) ^{\frac{3}{5}}} e^{x}

Simplify

\frac{2}{5 ( e ^{x} - 2 y ^{- 3} ) ^{\frac{3}{5}}} e^{x} : \frac{2 e ^{x} y ^{\frac{9}{5}}}{5 ( e ^{x} y ^{3} - 2 ) ^{\frac{3}{5}}}

= \frac{2 e ^{x} y ^{\frac{9}{5}}}{5 ( e ^{x} y ^{3} - 2 ) ^{\frac{3}{5}}}

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

f^{^{''}} (x) = 4 x

\int_{0}^{3} π (6 3 y)^{2} d y

(x^{2} + y^{2}) d x - x y d y = 0

\int \frac{6}{x} d x

What is (\partial)/(\partial x)((e^x-2y^{-3})^{2/5}) ?
The answer to (\partial)/(\partial x)((e^x-2y^{-3})^{2/5}) is (2e^xy^{9/5})/(5(e^xy^3-2)^{3/5)}