What is the derivative of sin(xy^2) ?

The derivative of sin(xy^2) is cos(xy^2)y^2

What is the first derivative of sin(xy^2) ?

The first derivative of sin(xy^2) is cos(xy^2)y^2

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derivative of

sin (x y^{2})

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

What is the derivative of sin(xy^2) ?
The derivative of sin(xy^2) is cos(xy^2)y^2
What is the first derivative of sin(xy^2) ?
The first derivative of sin(xy^2) is cos(xy^2)y^2