What is (\partial)/(\partial y)(ln(x^{10}y)) ?

The answer to (\partial)/(\partial y)(ln(x^{10}y)) is 1/y

Popular >

(\partial)/(\partial y)(ln(x^{10}y))

\frac{\partial}{\partial y} (ln (x^{10} y))

\frac{1}{y}

Solution steps

\frac{\partial}{\partial y} (ln (x^{10} y))

Treat

x

as a constant

Apply the chain rule:

\frac{1}{x ^{10} y} \frac{\partial}{\partial y} (x^{10} y)

= \frac{1}{x ^{10} y} \frac{\partial}{\partial y} (x^{10} y)

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

= \frac{1}{x ^{10} y} x^{10}

Simplify

\frac{1}{x ^{10} y} x^{10} : \frac{1}{y}

= \frac{1}{y}

66 x, \frac{2}{3} x, 40 - x^{2}

f (x) = \frac{1}{x ^{3}}, at x = - 2

\int_{- 2}^{6} 4 y - (y^{2} - 12) d y

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

\frac{\partial}{\partial x} (40 x y^{- 4} z)

What is (\partial)/(\partial y)(ln(x^{10}y)) ?
The answer to (\partial)/(\partial y)(ln(x^{10}y)) is 1/y