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

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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

What is the d/(dy)(sin(xy^2)) ?
The d/(dy)(sin(xy^2)) is cos(xy^2)*2xy
What is the first d/(dy)(sin(xy^2)) ?
The first d/(dy)(sin(xy^2)) is cos(xy^2)*2xy