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

The d/(dy)(sin(xy)) is cos(xy)x

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

The first d/(dy)(sin(xy)) is cos(xy)x

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

cos (x y) x

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

= cos (x y) x

\frac{A}{y ^{6}} + B e^{y}

\int_{- \infty}^{0} 2^{x} d x

a \to 0 lim (\frac{cos ( a )}{a})

\frac{\partial}{\partial x} (6 x^{9 y})

n = 0 \sum \infty \frac{e}{π}