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

The answer to (\partial)/(\partial z)(e^{xyz^8}) is e^{xyz^8}*8xyz^7

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

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

e^{x y z^{8}} \cdot 8 x y z^{7}

Solution steps

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

Treat

x, y

as constants

Apply the chain rule:

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

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

\frac{\partial}{\partial z} (x y z^{8}) = 8 x y z^{7}

= e^{x y z^{8}} \cdot 8 x y z^{7}

f (x) = 2 sin (x), g (x) = 2 cos (x)

y^{^{''}} + 2 y^{^{'}} + y = - 4 e^{- t}

y^{^{''}} + 9 y = 4 x e^{(2 x)}, y (0) = 0, y^{^{'}} (0) = 0

x \to 0 + lim (5 x + 9)

\int_{- 2}^{1} (x^{3} - 3 x + 2) d x

What is (\partial)/(\partial z)(e^{xyz^8}) ?
The answer to (\partial)/(\partial z)(e^{xyz^8}) is e^{xyz^8}*8xyz^7