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Popular >

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

Solution

\frac{d}{d x} (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

integral of 7x(x^6-1/7)

\int 7 x (x^{6} - \frac{1}{7}) d x

integral of x^{9/2}

\int x^{\frac{9}{2}} d x

(x-3)(dy)/(dx)=4(x-3)^4+y

(x - 3) \frac{d y}{d x} = 4 (x - 3)^{4} + y

(\partial)/(\partial y)(e^{yx^2})

\frac{\partial}{\partial y} (e^{y x^{2}})

integral of (70)/((x+1)(x^2+9)^2)

\int \frac{70}{( x + 1 ) ( x ^{2} + 9 ) ^{2}} d x

Frequently Asked Questions (FAQ)

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