What is (\partial)/(\partial y)(6xy-2+10x^2y) ?

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

(\partial)/(\partial y)(6xy-2+10x^2y)

\frac{\partial}{\partial y} (6 x y - 2 + 10 x^{2} y)

10 x^{2} + 6 x

Solution steps

\frac{\partial}{\partial y} (6 x y - 2 + 10 x^{2} y)

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (6 x y) - \frac{\partial}{\partial y} (2) + \frac{\partial}{\partial y} (10 x^{2} y)

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

\frac{\partial}{\partial y} (2) = 0

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

= 6 x - 0 + 10 x^{2}

Simplify

= 10 x^{2} + 6 x

\frac{d}{d x} (ln (sin^{3} (x^{2} + 7)))

y^{3} + x y^{2} - 61 = x + 3 y^{2}, at x = 3

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

\int cot (10 x) csc^{4} (10 z)

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

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