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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

\frac{d}{d x} (12 e^{2} x)

\frac{\partial}{\partial x} (y^{2} z cos (x))

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

\frac{\partial}{\partial x} (\frac{g ( x )}{x} - \frac{h ( x )}{x})

\int sec^{7} (x) tan (x) d x

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