What is (\partial)/(\partial x)(2xy^3+cos(y)) ?

The answer to (\partial)/(\partial x)(2xy^3+cos(y)) is 2y^3

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(\partial)/(\partial x)(2xy^3+cos(y))

\frac{\partial}{\partial x} (2 x y^{3} + cos (y))

2 y^{3}

Solution steps

\frac{\partial}{\partial x} (2 x y^{3} + cos (y))

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (2 x y^{3}) + \frac{\partial}{\partial x} (cos (y))

\frac{\partial}{\partial x} (2 x y^{3}) = 2 y^{3}

\frac{\partial}{\partial x} (cos (y)) = 0

= 2 y^{3} + 0

Simplify

= 2 y^{3}

\frac{\partial}{\partial x} (e^{y} e^{x} + ln (x y))

e^{s^{2} + 1}

\frac{d y}{d x} - \frac{1}{x} y = 1 - \frac{1}{x}

f (x) = cos (6 x)

\frac{tan ( 3 x )}{x ^{2}}

What is (\partial)/(\partial x)(2xy^3+cos(y)) ?
The answer to (\partial)/(\partial x)(2xy^3+cos(y)) is 2y^3