What is (\partial)/(\partial x)(e^{ax+by}) ?

The answer to (\partial)/(\partial x)(e^{ax+by}) is e^{ax+by}a

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(\partial)/(\partial x)(e^{ax+by})

\frac{\partial}{\partial x} (e^{a x + b y})

e^{a x + b y} a

Solution steps

\frac{\partial}{\partial x} (e^{a x + b y})

Treat

a, b, y

as constants

Apply the chain rule:

e^{a x + b y} \frac{\partial}{\partial x} (a x + b y)

= e^{a x + b y} \frac{\partial}{\partial x} (a x + b y)

\frac{\partial}{\partial x} (a x + b y) = a

= e^{a x + b y} a

What is (\partial)/(\partial x)(e^{ax+by}) ?
The answer to (\partial)/(\partial x)(e^{ax+by}) is e^{ax+by}a