What is (\partial)/(\partial x)(5x^2y+6xy^3) ?

The answer to (\partial)/(\partial x)(5x^2y+6xy^3) is 10yx+6y^3

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(\partial)/(\partial x)(5x^2y+6xy^3)

\frac{\partial}{\partial x} (5 x^{2} y + 6 x y^{3})

10 y x + 6 y^{3}

Solution steps

\frac{\partial}{\partial x} (5 x^{2} y + 6 x y^{3})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (5 x^{2} y) + \frac{\partial}{\partial x} (6 x y^{3})

\frac{\partial}{\partial x} (5 x^{2} y) = 10 y x

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

= 10 y x + 6 y^{3}

y^{^{'}} = 9 y^{2} sin (x)

f (x) = 3 x^{3} + 5 x^{2} + 5 x, at x = - 1

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

y = 2 x^{2}, y = 2 x + 6, - 2, 2

y \frac{d y}{d x} + 8 x^{3} = 4 x

What is (\partial)/(\partial x)(5x^2y+6xy^3) ?
The answer to (\partial)/(\partial x)(5x^2y+6xy^3) is 10yx+6y^3