What is (\partial)/(\partial y)(yln(x^2y)) ?

The answer to (\partial)/(\partial y)(yln(x^2y)) is ln(yx^2)+1

Popular >

(\partial)/(\partial y)(yln(x^2y))

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

ln (y x^{2}) + 1

Solution steps

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

Treat

x

as a constant

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = y, g = ln (x^{2} y)

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

\frac{\partial}{\partial y} (y) = 1

\frac{\partial}{\partial y} (ln (x^{2} y)) = \frac{1}{y}

= 1 \cdot ln (x^{2} y) + \frac{1}{y} y

Simplify

1 \cdot ln (x^{2} y) + \frac{1}{y} y : ln (y x^{2}) + 1

= ln (y x^{2}) + 1

\frac{\partial}{\partial x} (x e^{x y} + y e^{- x})

\int 1 - sin^{2} (θ) d θ

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

\int 4 y sin (x y) d x

\frac{d}{d x} (A (- 2 e^{- 2 x} x + e^{- 2 x}))

What is (\partial)/(\partial y)(yln(x^2y)) ?
The answer to (\partial)/(\partial y)(yln(x^2y)) is ln(yx^2)+1