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Popular Calculus >

derivative of ln(x^2+2-y)

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

(\partial)/(\partial x)(x/(sin(2x)+3y+z^2))

\frac{\partial}{\partial x} (\frac{x}{sin ( 2 x ) + 3 y + z ^{2}})

integral of sinh^3(x)

\int sinh^{3} (x) d x

limit as x approaches 0 of |x+2|

x \to 0 lim (∣ x + 2 ∣)

integral of sin^4(x/3)cos(x/3)

\int sin^{4} (\frac{x}{3}) cos (\frac{x}{3}) d x

implicit y^5=x^6

im pl i c i t y^{5} = x^{6}

Frequently Asked Questions (FAQ)

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