What is the d/(dy)(2xsin(y)) ?

The d/(dy)(2xsin(y)) is 2xcos(y)

What is the first d/(dy)(2xsin(y)) ?

The first d/(dy)(2xsin(y)) is 2xcos(y)

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\frac{d}{d y} (2 x sin (y))

2 x cos (y)

Solution steps

\frac{d}{d y} (2 x sin (y))

Treat

x

as a constant

Take the constant out:

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

= 2 x \frac{d}{d y} (sin (y))

Apply the common derivative:

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

= 2 x cos (y)

\frac{\partial}{\partial x} (- (x - 4)^{2} - (y - 1)^{2})

\int \frac{1}{x} d x

\int \frac{1}{81 + 16 x ^{2}} d x

y^{^{'}} + y = sin (2 t)

\frac{\partial}{\partial y} (x y + yz)