What is (\partial)/(\partial x)(2xy^3+4) ?

The answer to (\partial)/(\partial x)(2xy^3+4) is 2y^3

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(\partial)/(\partial x)(2xy^3+4)

\frac{\partial}{\partial x} (2 x y^{3} + 4)

2 y^{3}

Solution steps

\frac{\partial}{\partial x} (2 x y^{3} + 4)

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} (4)

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

\frac{\partial}{\partial x} (4) = 0

= 2 y^{3} + 0

Simplify

= 2 y^{3}

\frac{d y}{d x} = \frac{y + 2 x y}{x}

e x t re m e f (x) = r^{2} - 10 x^{2}

a re a e^{- 2 x}, x \geq 3

\int \frac{5}{21 x ^{2} - 2 x - 8} d x

t an g e n t x^{2} + 3 x - 1

What is (\partial)/(\partial x)(2xy^3+4) ?
The answer to (\partial)/(\partial x)(2xy^3+4) is 2y^3