What is (\partial)/(\partial x)(cos(xy^2)) ?

The answer to (\partial)/(\partial x)(cos(xy^2)) is -sin(xy^2)y^2

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(\partial)/(\partial x)(cos(xy^2))

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

- sin (x y^{2}) y^{2}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

= - sin (x y^{2}) y^{2}

y^{^{''}} + 4 y = e^{(- t)}

csc (x + 5)

\frac{d y}{d x} - (\frac{1 + x}{x}) y = \frac{y ^{2}}{x}

\int_{1}^{3} 4 d x

f (x) = sin (2 x^{3})

What is (\partial)/(\partial x)(cos(xy^2)) ?
The answer to (\partial)/(\partial x)(cos(xy^2)) is -sin(xy^2)y^2