What is (\partial)/(\partial x)(e^{xyz^7}) ?

The answer to (\partial)/(\partial x)(e^{xyz^7}) is e^{xyz^7}yz^7

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(\partial)/(\partial x)(e^{xyz^7})

\frac{\partial}{\partial x} (e^{x y z^{7}})

e^{x y z^{7}} y z^{7}

Solution steps

\frac{\partial}{\partial x} (e^{x y z^{7}})

Treat

y, z

as constants

Apply the chain rule:

e^{x y z^{7}} \frac{\partial}{\partial x} (x y z^{7})

= e^{x y z^{7}} \frac{\partial}{\partial x} (x y z^{7})

\frac{\partial}{\partial x} (x y z^{7}) = y z^{7}

= e^{x y z^{7}} y z^{7}

What is (\partial)/(\partial x)(e^{xyz^7}) ?
The answer to (\partial)/(\partial x)(e^{xyz^7}) is e^{xyz^7}yz^7