What is (\partial)/(\partial y)(e^{x-1}cos(y)) ?

The answer to (\partial)/(\partial y)(e^{x-1}cos(y)) is -e^{x-1}sin(y)

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(\partial)/(\partial y)(e^{x-1}cos(y))

\frac{\partial}{\partial y} (e^{x - 1} cos (y))

- e^{x - 1} sin (y)

Solution steps

\frac{\partial}{\partial y} (e^{x - 1} cos (y))

Treat

x

as a constant

Take the constant out:

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

= e^{x - 1} \frac{\partial}{\partial y} (cos (y))

Apply the common derivative:

\frac{\partial}{\partial y} (cos (y)) = - sin (y)

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

Simplify

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

\frac{\partial}{\partial x} (72 y^{7} x^{7} - 56 y^{6} x^{6})

\frac{1 - x}{1 + x}

x \to 0 lim (\frac{5 x + 6}{x})

x \to 3 + lim (\frac{x ^{2}}{9 - x ^{2}})

\int 1 x (4 - 2 (x - 3)) d x

What is (\partial)/(\partial y)(e^{x-1}cos(y)) ?
The answer to (\partial)/(\partial y)(e^{x-1}cos(y)) is -e^{x-1}sin(y)