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

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

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

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

4 x^{3} + 5 y^{3}

Solution steps

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

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

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

= 4 x^{3} + 5 y^{3}

\int \frac{x ^{2}}{x ^{2} + x + 30} d x

f (x) = 2 x + 3, at x = 3

\int_{0}^{π} 3 x^{2} + cos (x) d x

\frac{x}{x ^{- 1} + 12}

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

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