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

The answer to (\partial)/(\partial y)(x^4+5xy^3) is 15xy^2

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

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

15 x y^{2}

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial y} (5 x y^{3}) = 15 x y^{2}

= 0 + 15 x y^{2}

Simplify

= 15 x y^{2}

\frac{x}{7} - \frac{7}{x}

\frac{2 s + 12}{s ^{2} + 2 s + 5}

(5 x^{2} + 3)^{\frac{1}{4}}

\int \frac{5 x ^{4} + 5 x ^{3} + 2 x + 1}{x ^{2} + x} d x

x \to 0 lim (\frac{ln ( 1 + 2 x )}{x})

What is (\partial)/(\partial y)(x^4+5xy^3) ?
The answer to (\partial)/(\partial y)(x^4+5xy^3) is 15xy^2