What is (\partial)/(\partial x)(ae^{ax+y}) ?

The answer to (\partial)/(\partial x)(ae^{ax+y}) is a^2e^{ax+y}

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(\partial)/(\partial x)(ae^{ax+y})

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

a^{2} e^{a x + y}

Solution steps

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

Treat

a, y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

= a e^{a x + y} a

Simplify

a e^{a x + y} a : a^{2} e^{a x + y}

= a^{2} e^{a x + y}

What is (\partial)/(\partial x)(ae^{ax+y}) ?
The answer to (\partial)/(\partial x)(ae^{ax+y}) is a^2e^{ax+y}