What is (\partial)/(\partial x)(e^{5xyz-9}) ?

The answer to (\partial)/(\partial x)(e^{5xyz-9}) is e^{5xyz-9}*5yz

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(\partial)/(\partial x)(e^{5xyz-9})

\frac{\partial}{\partial x} (e^{5 x yz - 9})

e^{5 x yz - 9} \cdot 5 yz

Solution steps

\frac{\partial}{\partial x} (e^{5 x yz - 9})

Treat

y, z

as constants

Apply the chain rule:

e^{5 x yz - 9} \frac{\partial}{\partial x} (5 x yz - 9)

= e^{5 x yz - 9} \frac{\partial}{\partial x} (5 x yz - 9)

\frac{\partial}{\partial x} (5 x yz - 9) = 5 yz

= e^{5 x yz - 9} \cdot 5 yz

\frac{\partial}{\partial y} (\frac{1}{y + 2 z})

f (t) = t^{2} - t + 1

\frac{\partial}{\partial x} (\frac{y - x}{z})

\frac{d}{d x} ((x - 2) (x + 2))

t \frac{d y}{d t} - 3 y = \frac{4 t ^{5}}{t ^{2} + 4}

What is (\partial)/(\partial x)(e^{5xyz-9}) ?
The answer to (\partial)/(\partial x)(e^{5xyz-9}) is e^{5xyz-9}*5yz