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Popular >

derivative of y=ln(xsqrt(x^2-4))

Solution

derivative of

y = ln (x x^{2} - 4)

Solution

\frac{2 x ^{2} - 4}{x ( x ^{2} - 4 )}

Solution steps

\frac{d}{d x} (ln (x x^{2} - 4))

Apply the chain rule:

\frac{1}{x x ^{2} - 4} \frac{d}{d x} (x x^{2} - 4)

= \frac{1}{x x ^{2} - 4} \frac{d}{d x} (x x^{2} - 4)

\frac{d}{d x} (x x^{2} - 4) = \frac{2 x ^{2} - 4}{x ^{2} - 4}

= \frac{1}{x x ^{2} - 4} \cdot \frac{2 x ^{2} - 4}{x ^{2} - 4}

Simplify

\frac{1}{x x ^{2} - 4} \cdot \frac{2 x ^{2} - 4}{x ^{2} - 4} : \frac{2 x ^{2} - 4}{x ( x ^{2} - 4 )}

= \frac{2 x ^{2} - 4}{x ( x ^{2} - 4 )}

Popular Examples

tangent of f(x)=sqrt(x)+1/(sqrt(x^3))tangent of

f (x) = x + \frac{1}{x ^{3}}

integral of 3/(50+2t)

\int \frac{3}{50 + 2 t} d t

derivative of-2cos(x+3x^3)

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

derivative of sqrt(x^2+5x)

\frac{d}{d x} (x^{2} + 5 x)

integral from 0 to pi of sin(x/2)

\int_{0}^{π} sin (\frac{x}{2}) d x

Frequently Asked Questions (FAQ)

What is the derivative of y=ln(xsqrt(x^2-4)) ?
The derivative of y=ln(xsqrt(x^2-4)) is (2x^2-4)/(x(x^2-4))
What is the first derivative of y=ln(xsqrt(x^2-4)) ?
The first derivative of y=ln(xsqrt(x^2-4)) is (2x^2-4)/(x(x^2-4))