What is (\partial)/(\partial x)(5x^3y^2-xln(y)) ?

The answer to (\partial)/(\partial x)(5x^3y^2-xln(y)) is 15y^2x^2-ln(y)

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(\partial)/(\partial x)(5x^3y^2-xln(y))

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

15 y^{2} x^{2} - ln (y)

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 15 y^{2} x^{2} - ln (y)

d er i v a t i v e ln (e^{r x} + s)

d er i v a t i v e f (x) = x^{2} - 2 x - 2

\frac{\partial}{\partial x} (1 0^{- 2 x})

\int a rcco tan (x) d x

\frac{d}{d x} (6 x^{3} x csc (x))

What is (\partial)/(\partial x)(5x^3y^2-xln(y)) ?
The answer to (\partial)/(\partial x)(5x^3y^2-xln(y)) is 15y^2x^2-ln(y)