What is (\partial)/(\partial x)(2xy^3-1) ?

The answer to (\partial)/(\partial x)(2xy^3-1) is 2y^3

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(\partial)/(\partial x)(2xy^3-1)

\frac{\partial}{\partial x} (2 x y^{3} - 1)

2 y^{3}

Solution steps

\frac{\partial}{\partial x} (2 x y^{3} - 1)

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} (1)

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

\frac{\partial}{\partial x} (1) = 0

= 2 y^{3} - 0

Simplify

= 2 y^{3}

\frac{d y}{d t} = \frac{t}{y + 1}

\frac{d}{d t} (e^{t} (a cos (2 t) + cos (2 t)))

f (x) = - x + \frac{4}{x} + 1

f (x) = - 3 cos (x) - \frac{x ^{2}}{2} + 20

\frac{\partial}{\partial x} (u^{2})

What is (\partial)/(\partial x)(2xy^3-1) ?
The answer to (\partial)/(\partial x)(2xy^3-1) is 2y^3