What is the derivative of log_{10}(x^6+5) ?

The derivative of log_{10}(x^6+5) is (6x^5)/(ln(10)(x^6+5))

What is the first derivative of log_{10}(x^6+5) ?

The first derivative of log_{10}(x^6+5) is (6x^5)/(ln(10)(x^6+5))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

lo g_{10} (x^{6} + 5)

\frac{6 x ^{5}}{ln ( 10 ) ( x ^{6} + 5 )}

Solution steps

\frac{d}{d x} (lo g_{10} (x^{6} + 5))

Apply log rule:

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

= \frac{d}{d x} (\frac{ln ( x ^{6} + 5 )}{ln ( 10 )})

Take the constant out:

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

= \frac{1}{ln ( 10 )} \frac{d}{d x} (ln (x^{6} + 5))

Apply the chain rule:

\frac{1}{x ^{6} + 5} \frac{d}{d x} (x^{6} + 5)

= \frac{1}{x ^{6} + 5} \frac{d}{d x} (x^{6} + 5)

\frac{d}{d x} (x^{6} + 5) = 6 x^{5}

= \frac{1}{ln ( 10 )} \cdot \frac{1}{x ^{6} + 5} \cdot 6 x^{5}

Simplify

\frac{1}{ln ( 10 )} \cdot \frac{1}{x ^{6} + 5} \cdot 6 x^{5} : \frac{6 x ^{5}}{ln ( 10 ) ( x ^{6} + 5 )}

= \frac{6 x ^{5}}{ln ( 10 ) ( x ^{6} + 5 )}

What is the derivative of log_{10}(x^6+5) ?
The derivative of log_{10}(x^6+5) is (6x^5)/(ln(10)(x^6+5))
What is the first derivative of log_{10}(x^6+5) ?
The first derivative of log_{10}(x^6+5) is (6x^5)/(ln(10)(x^6+5))