What is the derivative of log_{10}(x^2-1) ?

The derivative of log_{10}(x^2-1) is (2x)/(ln(10)(x^2-1))

What is the first derivative of log_{10}(x^2-1) ?

The first derivative of log_{10}(x^2-1) is (2x)/(ln(10)(x^2-1))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

lo g_{10} (x^{2} - 1)

\frac{2 x}{ln ( 10 ) ( x ^{2} - 1 )}

Solution steps

\frac{d}{d x} (lo g_{10} (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 ( 10 )})

Take the constant out:

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

= \frac{1}{ln ( 10 )} \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) = 2 x

= \frac{1}{ln ( 10 )} \cdot \frac{1}{x ^{2} - 1} \cdot 2 x

Simplify

\frac{1}{ln ( 10 )} \cdot \frac{1}{x ^{2} - 1} \cdot 2 x : \frac{2 x}{ln ( 10 ) ( x ^{2} - 1 )}

= \frac{2 x}{ln ( 10 ) ( x ^{2} - 1 )}

(x^{2} + 1)^{4}

\frac{d}{d x} ((a + 3) \cdot x^{2} + (b - 2) \cdot x + c)

e^{- x} + 1

sin (x) ln (1 + x)

arcsin (2 x - 1)

What is the derivative of log_{10}(x^2-1) ?
The derivative of log_{10}(x^2-1) is (2x)/(ln(10)(x^2-1))
What is the first derivative of log_{10}(x^2-1) ?
The first derivative of log_{10}(x^2-1) is (2x)/(ln(10)(x^2-1))