Calculus Examples

$y = \log_{6} (x)$

Step 1

Differentiate both sides of the equation.

$\frac{d}{d x} (y) = \frac{d}{d x} (\log_{6} (x))$

Step 2

The derivative of $y$ with respect to $x$ is $y'$ .

$y'$

Step 3

The derivative of $\log_{6} (x)$ with respect to $x$ is $\frac{1}{x \ln (6)}$ .

$\frac{1}{x \ln (6)}$

Step 4

Reform the equation by setting the left side equal to the right side.

$y' = \frac{1}{x \ln (6)}$

Step 5

Replace $y'$ with $\frac{d y}{d x}$ .

$\frac{d y}{d x} = \frac{1}{x \ln (6)}$