What is (\partial)/(\partial x)(8x^2y+5xy^3) ?

The answer to (\partial)/(\partial x)(8x^2y+5xy^3) is 16yx+5y^3

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(\partial)/(\partial x)(8x^2y+5xy^3)

\frac{\partial}{\partial x} (8 x^{2} y + 5 x y^{3})

16 y x + 5 y^{3}

Solution steps

\frac{\partial}{\partial x} (8 x^{2} y + 5 x y^{3})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (8 x^{2} y) + \frac{\partial}{\partial x} (5 x y^{3})

\frac{\partial}{\partial x} (8 x^{2} y) = 16 y x

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

= 16 y x + 5 y^{3}

y = 7 x^{2} - 4 x, - 74

\int (x - 9)^{2} d x

\int_{0}^{\frac{π}{3}} tan^{5} (x) d x

y^{^{''}} + \frac{6}{x} y^{^{'}} + \frac{4}{x ^{2}} y = 0

f (x) = x^{2} - 4 x + 2

What is (\partial)/(\partial x)(8x^2y+5xy^3) ?
The answer to (\partial)/(\partial x)(8x^2y+5xy^3) is 16yx+5y^3