Evaluate Using the Given Value (dt)/(dx) if t=x/(8x-4)

$\frac{d t}{d x}$ if $t = \frac{x}{8 x - 4}$

Step 1

Factor $4$ out of $8 x - 4$ .

Factor $4$ out of $8 x$ .

$t = \frac{x}{4 (2 x) - 4}$

Factor $4$ out of $- 4$ .

$t = \frac{x}{4 (2 x) + 4 (- 1)}$

Factor $4$ out of $4 (2 x) + 4 (- 1)$ .

$t = \frac{x}{4 (2 x - 1)}$

Step 2

Replace the variable $t$ with $\frac{x}{4 (2 x - 1)}$ in the expression.

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

Step 3

Cancel the common factor of $d$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{\frac{x}{4 (2 x - 1)}}{x}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{x}{4 (2 x - 1)} \cdot \frac{1}{x}$

Step 5

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{x}{4 (2 x - 1)} \cdot \frac{1}{x}$

Rewrite the expression.

$\frac{1}{4 (2 x - 1)}$