What is the d/(dy)(e^x*sin(y)) ?

The d/(dy)(e^x*sin(y)) is e^xcos(y)

What is the first d/(dy)(e^x*sin(y)) ?

The first d/(dy)(e^x*sin(y)) is e^xcos(y)

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\frac{d}{d y} (e^{x} \cdot sin (y))

e^{x} cos (y)

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the common derivative:

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

= e^{x} cos (y)

4 y

y^{^{''}} - 10 y^{^{'}} + 25 y = 0

\frac{d y}{d x} + 15 x^{2} y = 30 x^{2}

n = 0 \sum \infty \frac{2 ^{n}}{n + 1}

\frac{s}{s ^{2} + 1}

What is the d/(dy)(e^x*sin(y)) ?
The d/(dy)(e^x*sin(y)) is e^xcos(y)
What is the first d/(dy)(e^x*sin(y)) ?
The first d/(dy)(e^x*sin(y)) is e^xcos(y)