What is the derivative of y=log_{2}(5x) ?

The derivative of y=log_{2}(5x) is 1/(ln(2)x)

What is the first derivative of y=log_{2}(5x) ?

The first derivative of y=log_{2}(5x) is 1/(ln(2)x)

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derivative of

y = lo g_{2} (5 x)

\frac{1}{ln ( 2 ) x}

Solution steps

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

Apply log rule:

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

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= \frac{1}{ln ( 2 )} \cdot \frac{1}{5 x} \cdot 5

Simplify

\frac{1}{ln ( 2 )} \cdot \frac{1}{5 x} \cdot 5 : \frac{1}{ln ( 2 ) x}

= \frac{1}{ln ( 2 ) x}

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

\int_{- 1}^{1} c (1 - x^{2}) d x

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

\frac{d y}{d x} = \frac{2 y}{x + 1}

x \to 1 lim (x + 4)

What is the derivative of y=log_{2}(5x) ?
The derivative of y=log_{2}(5x) is 1/(ln(2)x)
What is the first derivative of y=log_{2}(5x) ?
The first derivative of y=log_{2}(5x) is 1/(ln(2)x)