What is (\partial)/(\partial x)(100e^{(2x+3y)}) ?

The answer to (\partial)/(\partial x)(100e^{(2x+3y)}) is 200e^{2x+3y}

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(\partial)/(\partial x)(100e^{(2x+3y)})

\frac{\partial}{\partial x} (100 e^{(2 x + 3 y)})

200 e^{2 x + 3 y}

Solution steps

\frac{\partial}{\partial x} (100 e^{(2 x + 3 y)})

Treat

y

as a constant

Take the constant out:

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

= 100 \frac{\partial}{\partial x} (e^{2 x + 3 y})

Apply the chain rule:

e^{2 x + 3 y} \frac{\partial}{\partial x} (2 x + 3 y)

= e^{2 x + 3 y} \frac{\partial}{\partial x} (2 x + 3 y)

\frac{\partial}{\partial x} (2 x + 3 y) = 2

= 100 e^{2 x + 3 y} \cdot 2

Simplify

= 200 e^{2 x + 3 y}

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What is (\partial)/(\partial x)(100e^{(2x+3y)}) ?
The answer to (\partial)/(\partial x)(100e^{(2x+3y)}) is 200e^{2x+3y}