What is (\partial)/(\partial x)(e^{xyz^8}) ?

The answer to (\partial)/(\partial x)(e^{xyz^8}) is e^{xyz^8}yz^8

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(\partial)/(\partial x)(e^{xyz^8})

\frac{\partial}{\partial x} (e^{x y z^{8}})

e^{x y z^{8}} y z^{8}

Solution steps

\frac{\partial}{\partial x} (e^{x y z^{8}})

Treat

y, z

as constants

Apply the chain rule:

e^{x y z^{8}} \frac{\partial}{\partial x} (x y z^{8})

= e^{x y z^{8}} \frac{\partial}{\partial x} (x y z^{8})

\frac{\partial}{\partial x} (x y z^{8}) = y z^{8}

= e^{x y z^{8}} y z^{8}

\frac{\partial}{\partial x} (6 y^{2})

f (x) = (3 x^{2} - 5 x) e^{x}

f (t) = (t^{62} + 3 t + 3) (5 t^{2} + 4)

\frac{d}{d x} (ln (7 x))

\frac{\partial}{\partial x} ((x y - 1)^{2})

What is (\partial)/(\partial x)(e^{xyz^8}) ?
The answer to (\partial)/(\partial x)(e^{xyz^8}) is e^{xyz^8}yz^8