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Popular >

derivative of ln(x+sqrt(x^2-9))

Solution

\frac{d}{d x} (ln (x + x^{2} - 9))

Solution

\frac{1}{x ^{2} - 9}

Solution steps

\frac{d}{d x} (ln (x + x^{2} - 9))

Apply the chain rule:

\frac{1}{x + x ^{2} - 9} \frac{d}{d x} (x + x^{2} - 9)

= \frac{1}{x + x ^{2} - 9} \frac{d}{d x} (x + x^{2} - 9)

\frac{d}{d x} (x + x^{2} - 9) = 1 + \frac{x}{x ^{2} - 9}

= \frac{1}{x + x ^{2} - 9} (1 + \frac{x}{x ^{2} - 9})

Simplify

\frac{1}{x + x ^{2} - 9} (1 + \frac{x}{x ^{2} - 9}) : \frac{1}{x ^{2} - 9}

= \frac{1}{x ^{2} - 9}

Popular Examples

derivative of (x+1/(x^3+x-2))

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

derivative of xln(5x)

\frac{d}{d x} (x ln (5 x))

tangent of 3x^2-4x+6,\at x=2 tangent of

3 x^{2} - 4 x + 6, at x = 2

y^{''}+4y=0,y(0)=1,y(1)=0

y^{^{''}} + 4 y = 0, y (0) = 1, y (1) = 0

d/(dt)(ae^tcos(2t)+be^tsin(2t))

\frac{d}{d t} (a e^{t} cos (2 t) + b e^{t} sin (2 t))

Frequently Asked Questions (FAQ)

What is the derivative of ln(x+sqrt(x^2-9)) ?
The derivative of ln(x+sqrt(x^2-9)) is 1/(sqrt(x^2-9))
What is the first derivative of ln(x+sqrt(x^2-9)) ?
The first derivative of ln(x+sqrt(x^2-9)) is 1/(sqrt(x^2-9))