Solve (x*12.5*1.6667*0.4)/(1-x*12.5*1.6667*0.4)

$$( x \times 12.5 \times 1.6667 \times 0.4 ) / ( 1 - x \times 12.5 \times 1.6667 \times 0.4 )$$

Evaluate

$$-\frac{16667x}{16667x-2000}$$

Short Solution Steps

Multiply 12.5 and 1.6667 to get 20.83375.

$$\frac{x\times 20.83375\times 0.4}{1-x\times 12.5\times 1.6667\times 0.4}$$

Multiply 20.83375 and 0.4 to get 8.3335.

$$\frac{x\times 8.3335}{1-x\times 12.5\times 1.6667\times 0.4}$$

Multiply 12.5 and 1.6667 to get 20.83375.

$$\frac{x\times 8.3335}{1-x\times 20.83375\times 0.4}$$

Multiply 20.83375 and 0.4 to get 8.3335.

$$\frac{x\times 8.3335}{1-x\times 8.3335}$$

Multiply -1 and 8.3335 to get -8.3335.

$$\frac{x\times 8.3335}{1-8.3335x}$$

Differentiate w.r.t. x

$$\frac{33334000}{\left(16667x-2000\right)^{2}}$$