What is the derivative of log_{7}(6x-5) ?

The derivative of log_{7}(6x-5) is 6/(ln(7)(6x-5))

What is the first derivative of log_{7}(6x-5) ?

The first derivative of log_{7}(6x-5) is 6/(ln(7)(6x-5))

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\frac{d}{d x} (lo g_{7} (6 x - 5))

\frac{6}{ln ( 7 ) ( 6 x - 5 )}

Solution steps

\frac{d}{d x} (lo g_{7} (6 x - 5))

Apply log rule:

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

= \frac{d}{d x} (\frac{ln ( 6 x - 5 )}{ln ( 7 )})

Take the constant out:

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

= \frac{1}{ln ( 7 )} \frac{d}{d x} (ln (6 x - 5))

Apply the chain rule:

\frac{1}{6 x - 5} \frac{d}{d x} (6 x - 5)

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

\frac{d}{d x} (6 x - 5) = 6

= \frac{1}{ln ( 7 )} \cdot \frac{1}{6 x - 5} \cdot 6

Simplify

\frac{1}{ln ( 7 )} \cdot \frac{1}{6 x - 5} \cdot 6 : \frac{6}{ln ( 7 ) ( 6 x - 5 )}

= \frac{6}{ln ( 7 ) ( 6 x - 5 )}

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

3 x^{2} cos (2 x)

x \to 7 - lim (\frac{4 x}{x - 7})

\int sin (2 x) cos (2 x) d x

x y^{2} y^{^{'}} = y^{3} - 4 x^{3}

What is the derivative of log_{7}(6x-5) ?
The derivative of log_{7}(6x-5) is 6/(ln(7)(6x-5))
What is the first derivative of log_{7}(6x-5) ?
The first derivative of log_{7}(6x-5) is 6/(ln(7)(6x-5))