What is (\partial)/(\partial x)(e^{xyz^4}) ?

The answer to (\partial)/(\partial x)(e^{xyz^4}) is e^{xyz^4}yz^4

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(\partial)/(\partial x)(e^{xyz^4})

\frac{\partial}{\partial x} (e^{x y z^{4}})

e^{x y z^{4}} y z^{4}

Solution steps

\frac{\partial}{\partial x} (e^{x y z^{4}})

Treat

y, z

as constants

Apply the chain rule:

e^{x y z^{4}} \frac{\partial}{\partial x} (x y z^{4})

= e^{x y z^{4}} \frac{\partial}{\partial x} (x y z^{4})

\frac{\partial}{\partial x} (x y z^{4}) = y z^{4}

= e^{x y z^{4}} y z^{4}

\frac{d}{d x} (e^{3 x + 1})

\int \frac{1}{1 + x} d x

cos (x), 5

\frac{d}{d x} (x^{2} - 10 x + 24)

x \to 1 lim (x^{3} - 1)

What is (\partial)/(\partial x)(e^{xyz^4}) ?
The answer to (\partial)/(\partial x)(e^{xyz^4}) is e^{xyz^4}yz^4