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}

\frac{d}{d y} (\frac{cy ( x )}{x ^{2} + y ^{2}})

\int \frac{1}{tan ^{2} ( x ) + 1} d x

y^{^{''}} + 4 y^{^{'}} + 4 y = 0, y (1) = 0, y^{^{'}} (1) = 1

0.001 x^{3} + 0.2 x^{2} + 36 x + 300

\int e^{- x} cos (- x) d x

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