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

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

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

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

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

- sin (x y) x

Solution steps

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

Treat

x

as a constant

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

= - sin (x y) x

\frac{d y}{d t} = \frac{t}{t ^{2} y + y}

\frac{d ^{2}}{d x ^{2}} ((x^{2} + 6)^{4})

\int x^{\frac{- 1}{2}} d x

\int \frac{cos ^{2} ( x )}{sin ^{4} ( x )} d x

n = 3 \sum \infty \frac{5}{9 ^{n}}