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

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

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

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

e^{x + 3 y}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (x + 3 y) = 1

= e^{x + 3 y} \cdot 1

Simplify

= e^{x + 3 y}

\frac{3}{5} x^{\frac{5}{3}} - \frac{3}{4} x^{\frac{1}{3}} + 6

e - e^{x} + x^{e}

\int sin (x) (csc (x) + cot (x)) d x

\int (2 + x^{8})^{4} 8 x^{7} d x

\int \frac{1}{x ^{2} - 6 x + 13} d x

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