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

The d/(dy)(sin(2y)) is cos(2y)*2

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

The first d/(dy)(sin(2y)) is cos(2y)*2

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

cos (2 y) \cdot 2

Solution steps

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

Apply the chain rule:

cos (2 y) \frac{d}{d y} (2 y)

= cos (2 y) \frac{d}{d y} (2 y)

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

= cos (2 y) \cdot 2

y^{^{'''}} - y^{^{''}} - 16 y^{^{'}} + 16 y = 0

x \to 0 lim (\frac{sin ^{5} ( x )}{x})

\frac{\partial}{\partial y} (3 x^{2} - 5 y)

y^{^{'}} = \frac{x y ^{2} - 0.5 sin ( 2 x )}{y ( 1 - x ^{2} )}

y^{^{'''}} + 2 y^{^{''}} + y^{^{'}} = 0