What is the d/(dy)(e^xcos(xy)) ?

The d/(dy)(e^xcos(xy)) is -e^xxsin(xy)

What is the first d/(dy)(e^xcos(xy)) ?

The first d/(dy)(e^xcos(xy)) is -e^xxsin(xy)

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\frac{d}{d y} (e^{x} cos (x y))

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

Solution steps

\frac{d}{d y} (e^{x} cos (x y))

Treat

x

as a constant

Take the constant out:

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

= e^{x} \frac{d}{d y} (cos (x y))

Apply the chain rule:

- sin (x y) \frac{d}{d y} (x y)

= - sin (x y) \frac{d}{d y} (x y)

\frac{d}{d y} (x y) = x

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

Simplify

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

What is the d/(dy)(e^xcos(xy)) ?
The d/(dy)(e^xcos(xy)) is -e^xxsin(xy)
What is the first d/(dy)(e^xcos(xy)) ?
The first d/(dy)(e^xcos(xy)) is -e^xxsin(xy)