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Popular >

derivative of ln(x^2-16x)

Solution

\frac{d}{d x} (ln (x^{2} - 16 x))

Solution

\frac{2 x - 16}{x ^{2} - 16 x}

Solution steps

\frac{d}{d x} (ln (x^{2} - 16 x))

Apply the chain rule:

\frac{1}{x ^{2} - 16 x} \frac{d}{d x} (x^{2} - 16 x)

= \frac{1}{x ^{2} - 16 x} \frac{d}{d x} (x^{2} - 16 x)

\frac{d}{d x} (x^{2} - 16 x) = 2 x - 16

= \frac{1}{x ^{2} - 16 x} (2 x - 16)

Simplify

\frac{1}{x ^{2} - 16 x} (2 x - 16) : \frac{2 x - 16}{x ^{2} - 16 x}

= \frac{2 x - 16}{x ^{2} - 16 x}

Popular Examples

integral of (x^2+3x-4)/(x^2-2x-8)

\int \frac{x ^{2} + 3 x - 4}{x ^{2} - 2 x - 8} d x

integral of (y^2-1)

\int (y^{2} - 1) d y

area x^3-13x^2+40x,-x^3+13x^2-40x area

x^{3} - 13 x^{2} + 40 x, - x^{3} + 13 x^{2} - 40 x

integral of sqrt(900-36x^2)

\int 900 - 36 x^{2} d x

y^{^{'}} = 13 x y - 16 x

Frequently Asked Questions (FAQ)

What is the derivative of ln(x^2-16x) ?
The derivative of ln(x^2-16x) is (2x-16)/(x^2-16x)
What is the first derivative of ln(x^2-16x) ?
The first derivative of ln(x^2-16x) is (2x-16)/(x^2-16x)