What is (\partial)/(\partial x)(e^{5xyz-3}) ?

The answer to (\partial)/(\partial x)(e^{5xyz-3}) is e^{5xyz-3}*5yz

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(\partial)/(\partial x)(e^{5xyz-3})

\frac{\partial}{\partial x} (e^{5 x yz - 3})

e^{5 x yz - 3} \cdot 5 yz

Solution steps

\frac{\partial}{\partial x} (e^{5 x yz - 3})

Treat

y, z

as constants

Apply the chain rule:

e^{5 x yz - 3} \frac{\partial}{\partial x} (5 x yz - 3)

= e^{5 x yz - 3} \frac{\partial}{\partial x} (5 x yz - 3)

\frac{\partial}{\partial x} (5 x yz - 3) = 5 yz

= e^{5 x yz - 3} \cdot 5 yz

What is (\partial)/(\partial x)(e^{5xyz-3}) ?
The answer to (\partial)/(\partial x)(e^{5xyz-3}) is e^{5xyz-3}*5yz