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

The derivative of cos(xy^2) is -sin(xy^2)(y^2+2xy(dy)/(dx))

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

The first derivative of cos(xy^2) is -sin(xy^2)(y^2+2xy(dy)/(dx))

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

What is the derivative of cos(xy^2) ?
The derivative of cos(xy^2) is -sin(xy^2)(y^2+2xy(dy)/(dx))
What is the first derivative of cos(xy^2) ?
The first derivative of cos(xy^2) is -sin(xy^2)(y^2+2xy(dy)/(dx))