What is (\partial)/(\partial x)(y{f}(x)+2x^3) ?

The answer to (\partial)/(\partial x)(y{f}(x)+2x^3) is y(\partial)/(\partial x)({f}(x))+6x^2

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(\partial)/(\partial x)(y{f}(x)+2x^3)

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

y \frac{\partial}{\partial x} (f (x)) + 6 x^{2}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (y f (x)) = y \frac{\partial}{\partial x} (f (x))

\frac{\partial}{\partial x} (2 x^{3}) = 6 x^{2}

= y \frac{\partial}{\partial x} (f (x)) + 6 x^{2}

e^{1 - x} \cdot (5 - x^{2})

f (x) = (7 x^{4} - 6 x^{3} - 5 x)^{8}

\int 120 x \cdot (2 x + 1)^{4} d x

\int \frac{1}{3} e^{- \frac{x}{2}} (x + 1) d x

\int sec^{8} (t) an x d x

What is (\partial)/(\partial x)(y{f}(x)+2x^3) ?
The answer to (\partial)/(\partial x)(y{f}(x)+2x^3) is y(\partial)/(\partial x)({f}(x))+6x^2