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

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

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

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

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

cos (y^{2}) \cdot 2 y

Solution steps

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

Apply the chain rule:

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

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

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

= cos (y^{2}) \cdot 2 y

\frac{\partial}{\partial x} (n ln (θ + 2))

\int x^{2} - 3 d x

f (x) = \frac{x}{1 + x ^{2}}, 0, at x = 0

\frac{d}{d x} (\frac{x ^{3}}{3} + \frac{x ^{2}}{2} - 2 x + 7)

(sec (x)) \frac{d y}{d x} + y = 2