What is (\partial)/(\partial x)(y^4+5xy^3) ?

The answer to (\partial)/(\partial x)(y^4+5xy^3) is 5y^3

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(\partial)/(\partial x)(y^4+5xy^3)

\frac{\partial}{\partial x} (y^{4} + 5 x y^{3})

5 y^{3}

Solution steps

\frac{\partial}{\partial x} (y^{4} + 5 x y^{3})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (y^{4}) + \frac{\partial}{\partial x} (5 x y^{3})

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

\frac{\partial}{\partial x} (5 x y^{3}) = 5 y^{3}

= 0 + 5 y^{3}

Simplify

= 5 y^{3}

\frac{d}{d x} (cos (5 x - 3))

\frac{- 2 x}{( x ^{2} - 1 ) ^{2}}

\int \frac{4 e ^{x}}{e ^{2 x} + 4 e ^{x} + 4} d x

\frac{d y}{d t} - \frac{1}{2} y = t y^{- 1}

\int e^{- 0.12 x} d x

What is (\partial)/(\partial x)(y^4+5xy^3) ?
The answer to (\partial)/(\partial x)(y^4+5xy^3) is 5y^3