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

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

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

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

2 x ln (y) + 5 y^{3}

Solution steps

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

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

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

= 2 x ln (y) + 5 y^{3}

x^{2} 8 x - 1

\frac{1 - 2 x}{4 + x}

\frac{d}{d x} (e^{x} cos (2 x) - 2 e^{x} sin (2 x))

\frac{\partial}{\partial y} (2 y)

\int \frac{3}{x 4 - x ^{2}} d x

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