What is the d/(dy)(ysin(xy)) ?

The d/(dy)(ysin(xy)) is sin(yx)+yxcos(yx)

What is the first d/(dy)(ysin(xy)) ?

The first d/(dy)(ysin(xy)) is sin(yx)+yxcos(yx)

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

sin (y x) + y x cos (y x)

Solution steps

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

Treat

x

as a constant

Apply the Product Rule:

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

f = y, g = sin (x y)

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

\frac{d y}{d y} = 1

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

= 1 \cdot sin (x y) + cos (x y) x y

Simplify

= sin (y x) + y x cos (y x)

x^{2} + 4, - x^{2} - 1, [0, 1]

\frac{d y}{d x} = \frac{2 x y + 2 x}{x ^{2} + 1}

\int_{1}^{\infty} \frac{1}{x ^{8}} d x

\frac{\partial}{\partial x} (4 x y - 3 x^{2})

y^{^{'}} = 2 x, y (1) = 7

What is the d/(dy)(ysin(xy)) ?
The d/(dy)(ysin(xy)) is sin(yx)+yxcos(yx)
What is the first d/(dy)(ysin(xy)) ?
The first d/(dy)(ysin(xy)) is sin(yx)+yxcos(yx)