What is (\partial)/(\partial x)(e^{4x+5y}) ?

The answer to (\partial)/(\partial x)(e^{4x+5y}) is e^{4x+5y}*4

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(\partial)/(\partial x)(e^{4x+5y})

\frac{\partial}{\partial x} (e^{4 x + 5 y})

e^{4 x + 5 y} \cdot 4

Solution steps

\frac{\partial}{\partial x} (e^{4 x + 5 y})

Treat

y

as a constant

Apply the chain rule:

e^{4 x + 5 y} \frac{\partial}{\partial x} (4 x + 5 y)

= e^{4 x + 5 y} \frac{\partial}{\partial x} (4 x + 5 y)

\frac{\partial}{\partial x} (4 x + 5 y) = 4

= e^{4 x + 5 y} \cdot 4

What is (\partial)/(\partial x)(e^{4x+5y}) ?
The answer to (\partial)/(\partial x)(e^{4x+5y}) is e^{4x+5y}*4