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

The answer to (\partial)/(\partial x)(sin(xyz^3)) is cos(xyz^3)yz^3

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

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

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

Solution steps

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

Treat

y, z

as constants

Apply the chain rule:

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

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

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

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

\int_{0}^{5} e^{3 x} d x

4 y^{^{''}} - 16 y^{^{'}} + 19 y = 0

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

\frac{y ^{^{'}}}{y} = x

\frac{6 x}{2 + x ^{2}}

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