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Popular >

derivative of ln(y-x^2)

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

integral of x*e^{x^2+1}

\int x \cdot e^{x^{2} + 1} d x

(5x+ye^{y/x})dx-(xe^{y/x})dy=0,y(1)=3

(5 x + y e^{\frac{y}{x}}) d x - (x e^{\frac{y}{x}}) d y = 0, y (1) = 3

integral of (3x)/(1-x^2)

\int \frac{3 x}{1 - x ^{2}} d x

(\partial)/(\partial y)(xye^{-7y})

\frac{\partial}{\partial y} (x y e^{- 7 y})

integral of (2x^4x+3x^3-x^2)/(x^3)

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

Frequently Asked Questions (FAQ)

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