What is (\partial)/(\partial x)(sin(xy^3)) ?

The answer to (\partial)/(\partial x)(sin(xy^3)) is cos(xy^3)y^3

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(\partial)/(\partial x)(sin(xy^3))

\frac{\partial}{\partial x} (sin (x y^{3}))

cos (x y^{3}) y^{3}

Solution steps

\frac{\partial}{\partial x} (sin (x y^{3}))

Treat

y

as a constant

Apply the chain rule:

cos (x y^{3}) \frac{\partial}{\partial x} (x y^{3})

= cos (x y^{3}) \frac{\partial}{\partial x} (x y^{3})

\frac{\partial}{\partial x} (x y^{3}) = y^{3}

= cos (x y^{3}) y^{3}

\int x^{3} (5 + x^{4})^{5} d x

8 (t + 1) \frac{d y}{d t} - 6 y = 12 t

\int_{0}^{1} (1 + 2^{x})^{2} 2^{- x} d x

\frac{\partial}{\partial x} (\cdot e)

What is (\partial)/(\partial x)(sin(xy^3)) ?
The answer to (\partial)/(\partial x)(sin(xy^3)) is cos(xy^3)y^3