What is the derivative of log_{9}(-(x-4(5x-2))) ?

The derivative of log_{9}(-(x-4(5x-2))) is -(-5x+11)/(ln(3)(x-4)(5x-2))

What is the first derivative of log_{9}(-(x-4(5x-2))) ?

The first derivative of log_{9}(-(x-4(5x-2))) is -(-5x+11)/(ln(3)(x-4)(5x-2))

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_{9} (- (x - 4) (5 x - 2)))

- \frac{- 5 x + 11}{ln ( 3 ) ( x - 4 ) ( 5 x - 2 )}

Solution steps

\frac{d}{d x} (lo g_{9} (- (x - 4) (5 x - 2)))

Apply log rule:

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

= \frac{d}{d x} (\frac{ln ( - ( x - 4 ) ( 5 x - 2 ) )}{ln ( 9 )})

Take the constant out:

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

= \frac{1}{ln ( 9 )} \frac{d}{d x} (ln (- (x - 4) (5 x - 2)))

Apply the chain rule:

\frac{1}{- ( x - 4 ) ( 5 x - 2 )} \frac{d}{d x} (- (x - 4) (5 x - 2))

= \frac{1}{- ( x - 4 ) ( 5 x - 2 )} \frac{d}{d x} (- (x - 4) (5 x - 2))

\frac{d}{d x} (- (x - 4) (5 x - 2)) = - 10 x + 22

= \frac{1}{ln ( 9 )} \cdot \frac{1}{- ( x - 4 ) ( 5 x - 2 )} (- 10 x + 22)

Simplify

\frac{1}{ln ( 9 )} \cdot \frac{1}{- ( x - 4 ) ( 5 x - 2 )} (- 10 x + 22) : - \frac{- 5 x + 11}{ln ( 3 ) ( x - 4 ) ( 5 x - 2 )}

= - \frac{- 5 x + 11}{ln ( 3 ) ( x - 4 ) ( 5 x - 2 )}

\frac{\partial}{\partial y} (sin (x) y)

f (x) = \frac{x ^{5} + x ^{9}}{x}

y = 8 e^{- x} + e^{3 x}

x \to 0 lim (1 - \frac{cos ( x )}{x})

\frac{5 + x - 5}{x}

What is the derivative of log_{9}(-(x-4(5x-2))) ?
The derivative of log_{9}(-(x-4(5x-2))) is -(-5x+11)/(ln(3)(x-4)(5x-2))
What is the first derivative of log_{9}(-(x-4(5x-2))) ?
The first derivative of log_{9}(-(x-4(5x-2))) is -(-5x+11)/(ln(3)(x-4)(5x-2))