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Popular >

derivative of ln(x^2-1/(x^2)-5)

Solution

\frac{d}{d x} (ln (x^{2}) - \frac{1}{x ^{2}} - 5)

Solution

\frac{2}{x} + \frac{2}{x ^{3}}

Solution steps

\frac{d}{d x} (ln (x^{2}) - \frac{1}{x ^{2}} - 5)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (ln (x^{2})) - \frac{d}{d x} (\frac{1}{x ^{2}}) - \frac{d}{d x} (5)

\frac{d}{d x} (ln (x^{2})) = \frac{2}{x}

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

\frac{d}{d x} (5) = 0

= \frac{2}{x} - (- \frac{2}{x ^{3}}) - 0

Simplify

= \frac{2}{x} + \frac{2}{x ^{3}}

Popular Examples

derivative of (x^2/(x^2-5))

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

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

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

derivative of 2^zlog_{2}(z)derivative of

2^{z} lo g_{2} (z)

y^'+((3y)/((300-t)))=4

y^{^{'}} + (\frac{3 y}{( 300 - t )}) = 4

integral of (sqrt(64x^2-1))/x

\int \frac{64 x ^{2} - 1}{x} d x

Frequently Asked Questions (FAQ)

What is the derivative of ln(x^2-1/(x^2)-5) ?
The derivative of ln(x^2-1/(x^2)-5) is 2/x+2/(x^3)
What is the first derivative of ln(x^2-1/(x^2)-5) ?
The first derivative of ln(x^2-1/(x^2)-5) is 2/x+2/(x^3)