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Popular >

derivative of ln(sqrt(x^2-7))

Solution

derivative of

ln (x^{2} - 7)

Solution

\frac{x}{x ^{2} - 7}

Solution steps

\frac{d}{d x} (ln (x^{2} - 7))

Apply the chain rule:

\frac{1}{x ^{2} - 7} \frac{d}{d x} (x^{2} - 7)

= \frac{1}{x ^{2} - 7} \frac{d}{d x} (x^{2} - 7)

\frac{d}{d x} (x^{2} - 7) = \frac{x}{x ^{2} - 7}

= \frac{1}{x ^{2} - 7} \cdot \frac{x}{x ^{2} - 7}

Simplify

\frac{1}{x ^{2} - 7} \cdot \frac{x}{x ^{2} - 7} : \frac{x}{x ^{2} - 7}

= \frac{x}{x ^{2} - 7}

Popular Examples

integral of (x-1)/(sqrt(1-x^2))

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

derivative of f(x)=x^2+8x+7

\frac{d}{d x} f (x) = x^{2} + 8 x + 7

limit as x approaches 0 of (7x^5+5x^2+12x)/(3x^5+4x)

x \to 0 lim (\frac{7 x ^{5} + 5 x ^{2} + 12 x}{3 x ^{5} + 4 x})

tangent of x^2-3xy=10 tangent of

x^{2} - 3 x y = 10

y^'=(sec(y))/((x-3)^2)

y^{^{'}} = \frac{sec ( y )}{( x - 3 ) ^{2}}

Frequently Asked Questions (FAQ)

What is the derivative of ln(sqrt(x^2-7)) ?
The derivative of ln(sqrt(x^2-7)) is x/(x^2-7)
What is the first derivative of ln(sqrt(x^2-7)) ?
The first derivative of ln(sqrt(x^2-7)) is x/(x^2-7)