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

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

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

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

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derivative of

lo g_{2} (3 - 2 x)

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

Solution steps

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

Apply log rule:

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

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

(\frac{1}{1 + x})^{^{'}}

x \to 0 lim (1 + csc (x))

\int (sec (x) + tan (x)) d x

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

\int_{7}^{8} x x - 7 d x

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