What is (\partial)/(\partial x)(e^{(3x+5y)}) ?

The answer to (\partial)/(\partial x)(e^{(3x+5y)}) is e^{3x+5y}*3

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(\partial)/(\partial x)(e^{(3x+5y)})

\frac{\partial}{\partial x} (e^{(3 x + 5 y)})

e^{3 x + 5 y} \cdot 3

Solution steps

\frac{\partial}{\partial x} (e^{(3 x + 5 y)})

Treat

y

as a constant

Apply the chain rule:

e^{3 x + 5 y} \frac{\partial}{\partial x} (3 x + 5 y)

= e^{3 x + 5 y} \frac{\partial}{\partial x} (3 x + 5 y)

\frac{\partial}{\partial x} (3 x + 5 y) = 3

= e^{3 x + 5 y} \cdot 3

\frac{d}{d x} (x \cdot e^{x} + e^{x})

\frac{d}{d x} ((\frac{x ^{2} + 4}{x ^{2} - 4})^{4})

\int \frac{( x ^{2} - 3 x + 1 )}{x ^{2} + x} d x

\int tan^{9} (x) d x

What is (\partial)/(\partial x)(e^{(3x+5y)}) ?
The answer to (\partial)/(\partial x)(e^{(3x+5y)}) is e^{3x+5y}*3