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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d}{d x} (\frac{x - 3}{x - 2}) = \frac{1}{( x - 2 ) ^{2}}

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

Simplify

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

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

Graph

Popular Examples

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

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\int \frac{1}{25 x ^{2} - 49} d x

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\int \frac{6 - x}{4 x ^{2} - 12 x + 7} d x

Frequently Asked Questions (FAQ)

What is the derivative of ln(x-2+(x-3)/(x-2)) ?
The derivative of ln(x-2+(x-3)/(x-2)) is (x-1)/((x-2)^2)
What is the first derivative of ln(x-2+(x-3)/(x-2)) ?
The first derivative of ln(x-2+(x-3)/(x-2)) is (x-1)/((x-2)^2)