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Popular >

derivative of ln(x+sqrt(x^2-6))

Solution

\frac{d}{d x} (ln (x + x^{2} - 6))

Solution

\frac{1}{x ^{2} - 6}

Solution steps

\frac{d}{d x} (ln (x + x^{2} - 6))

Apply the chain rule:

\frac{1}{x + x ^{2} - 6} \frac{d}{d x} (x + x^{2} - 6)

= \frac{1}{x + x ^{2} - 6} \frac{d}{d x} (x + x^{2} - 6)

\frac{d}{d x} (x + x^{2} - 6) = 1 + \frac{x}{x ^{2} - 6}

= \frac{1}{x + x ^{2} - 6} (1 + \frac{x}{x ^{2} - 6})

Simplify

\frac{1}{x + x ^{2} - 6} (1 + \frac{x}{x ^{2} - 6}) : \frac{1}{x ^{2} - 6}

= \frac{1}{x ^{2} - 6}

Popular Examples

integral of+(40)/(1-cos(8x))

\int + \frac{40}{1 - cos ( 8 x )} d x

(\partial)/(\partial x)(sqrt(9-x^2-y^2))

\frac{\partial}{\partial x} (9 - x^{2} - y^{2})

derivative of ln((x^2/(2x^2+3x+2)))

\frac{d}{d x} (ln (\frac{x ^{2}}{2 x ^{2} + 3 x + 2}))

tangent of y= pi/((2x)^4)tangent of

y = \frac{π}{( 2 x ) ^{4}}

integral of 2/(x^2+9)

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

Frequently Asked Questions (FAQ)

What is the derivative of ln(x+sqrt(x^2-6)) ?
The derivative of ln(x+sqrt(x^2-6)) is 1/(sqrt(x^2-6))
What is the first derivative of ln(x+sqrt(x^2-6)) ?
The first derivative of ln(x+sqrt(x^2-6)) is 1/(sqrt(x^2-6))