What is the derivative of log_{10}((x-3^2)) ?

The derivative of log_{10}((x-3^2)) is 2/(ln(10)(x-3))

What is the first derivative of log_{10}((x-3^2)) ?

The first derivative of log_{10}((x-3^2)) is 2/(ln(10)(x-3))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (lo g_{10} ((x - 3)^{2}))

\frac{2}{ln ( 10 ) ( x - 3 )}

Solution steps

\frac{d}{d x} (lo g_{10} ((x - 3)^{2}))

Apply log rule:

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

= \frac{d}{d x} \frac{ln ( ( x - 3 ) ^{2} )}{ln ( 10 )}

Take the constant out:

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

= \frac{1}{ln ( 10 )} \frac{d}{d x} (ln ((x - 3)^{2}))

Apply the chain rule:

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

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

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

= \frac{1}{ln ( 10 )} \cdot \frac{1}{( x - 3 ) ^{2}} \cdot 2 (x - 3)

Simplify

\frac{1}{ln ( 10 )} \cdot \frac{1}{( x - 3 ) ^{2}} \cdot 2 (x - 3) : \frac{2}{ln ( 10 ) ( x - 3 )}

= \frac{2}{ln ( 10 ) ( x - 3 )}

\int \frac{4 x ^{2} + 1}{2 x + 5} d x

\int e^{- \frac{3}{2} t} d t

3 x^{2} + 4 x + 8

(x^{2} + 7)^{5}

x, x^{3} - x^{2} - x

What is the derivative of log_{10}((x-3^2)) ?
The derivative of log_{10}((x-3^2)) is 2/(ln(10)(x-3))
What is the first derivative of log_{10}((x-3^2)) ?
The first derivative of log_{10}((x-3^2)) is 2/(ln(10)(x-3))