What is the derivative of log_{5}(sqrt(x^2-1)) ?

The derivative of log_{5}(sqrt(x^2-1)) is x/(ln(5)(x^2-1))

What is the first derivative of log_{5}(sqrt(x^2-1)) ?

The first derivative of log_{5}(sqrt(x^2-1)) is x/(ln(5)(x^2-1))

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derivative of

lo g_{5} (x^{2} - 1)

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

Solution steps

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

Apply log rule:

lo g_{a} (b) = \frac{ln ( b )}{ln ( a )}

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

x \to 1 lim (- x^{2} - 1)

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

\int 20 x e^{8 x} d x

\frac{d y}{d t} = \frac{y}{t + 1} + 4 t^{2} + 4 t

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

What is the derivative of log_{5}(sqrt(x^2-1)) ?
The derivative of log_{5}(sqrt(x^2-1)) is x/(ln(5)(x^2-1))
What is the first derivative of log_{5}(sqrt(x^2-1)) ?
The first derivative of log_{5}(sqrt(x^2-1)) is x/(ln(5)(x^2-1))