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

The answer to (\partial)/(\partial x)(e^{xyz^3}) is e^{xyz^3}yz^3

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(\partial)/(\partial x)(e^{xyz^3})

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

e^{x y z^{3}} y z^{3}

Solution steps

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

Treat

y, z

as constants

Apply the chain rule:

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

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

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

= e^{x y z^{3}} y z^{3}

What is (\partial)/(\partial x)(e^{xyz^3}) ?
The answer to (\partial)/(\partial x)(e^{xyz^3}) is e^{xyz^3}yz^3