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

The answer to (\partial)/(\partial x)(e^{(x^2)/(y^3)}) is (2e^{\frac{x^2)/(y^3)}x}{y^3}

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

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

\frac{2 e ^{\frac{x ^{2}}{y ^{3}}} x}{y ^{3}}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

= e^{\frac{x ^{2}}{y ^{3}}} \frac{2 x}{y ^{3}}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 e ^{\frac{x ^{2}}{y ^{3}}} x}{y ^{3}}

\int 6 x^{5} - 4 x^{2} + \frac{7}{3} d x

t \to 0 lim (f (t))

\frac{d}{d x} (\frac{2 x - 3}{x - 1})

x \to 0 lim (e^{- 2 f (x)})

\frac{\partial}{\partial x} (\frac{1}{1 - y})

What is (\partial)/(\partial x)(e^{(x^2)/(y^3)}) ?
The answer to (\partial)/(\partial x)(e^{(x^2)/(y^3)}) is (2e^{\frac{x^2)/(y^3)}x}{y^3}