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

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

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

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

- e^{3 x - y}

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

= e^{3 x - y} (- 1)

Simplify

= - e^{3 x - y}

\int x e^{2 - x} d x

\int \frac{1}{3} x d x

y = x^{2} sin (2 x)

\frac{d}{d x} (\frac{a}{( x ^{2} + a ^{2} ) ^{2}})

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

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