What is the d/(dy)(e^ycos(y)) ?

The d/(dy)(e^ycos(y)) is e^ycos(y)-e^ysin(y)

What is the first d/(dy)(e^ycos(y)) ?

The first d/(dy)(e^ycos(y)) is e^ycos(y)-e^ysin(y)

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

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{y}, g = cos (y)

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

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

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

= e^{y} cos (y) + (- sin (y)) e^{y}

Simplify

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

\int tan^{2} (x) sec^{6} (x) d x

\int x (x^{2} + 1)^{100} d x

\frac{x ^{2} - 10 x + 65}{x - 8}

n = 0 \sum \infty \frac{1}{( 2 n - 1 ) ^{2}}

\frac{d}{d x} (ln (cos (9 x)))

What is the d/(dy)(e^ycos(y)) ?
The d/(dy)(e^ycos(y)) is e^ycos(y)-e^ysin(y)
What is the first d/(dy)(e^ycos(y)) ?
The first d/(dy)(e^ycos(y)) is e^ycos(y)-e^ysin(y)