en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of ln(x-y^2)

Solution

\frac{d}{d x} (ln (x - y^{2}))

Solution

\frac{1 - 2 y \frac{d y}{d x}}{x - y ^{2}}

Solution steps

\frac{d}{d x} (ln (x - y^{2}))

Apply the chain rule:

\frac{1}{x - y ^{2}} \frac{d}{d x} (x - y^{2})

= \frac{1}{x - y ^{2}} \frac{d}{d x} (x - y^{2})

\frac{d}{d x} (x - y^{2}) = 1 - 2 y \frac{d y}{d x}

= \frac{1}{x - y ^{2}} (1 - 2 y \frac{d y}{d x})

Simplify

\frac{1}{x - y ^{2}} (1 - 2 y \frac{d y}{d x}) : \frac{1 - 2 y \frac{d y}{d x}}{x - y ^{2}}

= \frac{1 - 2 y \frac{d y}{d x}}{x - y ^{2}}

Popular Examples

integral of 7/(x^2sqrt(x^2+9))

\int \frac{7}{x ^{2} x ^{2} + 9} d x

integral of 1/(y(1-y))

\int \frac{1}{y ( 1 - y )} d y

integral of (1/(x^2-x))

\int (\frac{1}{x ^{2} - x}) d x

(2 + x) y^{^{'}} = 8 y

limit as x approaches 0 of e^x-e^{-x}

x \to 0 lim (e^{x} - e^{- x})

Frequently Asked Questions (FAQ)

What is the derivative of ln(x-y^2) ?
The derivative of ln(x-y^2) is (1-2y\frac{dy)/(dx)}{x-y^2}
What is the first derivative of ln(x-y^2) ?
The first derivative of ln(x-y^2) is (1-2y\frac{dy)/(dx)}{x-y^2}