Solve 2550000/12*15/100*x

$$\frac{ 2550000 }{ 12 } \times \frac{ 15 }{ 100 \times x }$$

Evaluate

$$\frac{31875}{x}$$

Solution Steps

Divide 2550000 by 12 to get 212500.

$$212500\times \frac{15}{100x}$$

Express 212500\times \frac{15}{100x} as a single fraction.

$$\frac{212500\times 15}{100x}$$

Cancel out 100 in both numerator and denominator.

$$\frac{15\times 2125}{x}$$

Multiply 15 and 2125 to get 31875.

$$\frac{31875}{x}$$

Differentiate w.r.t. x

$$-\frac{31875}{x^{2}}$$

Steps Using Definition of a Derivative

Divide 2550000 by 12 to get 212500.

$$\frac{\mathrm{d}}{\mathrm{d}x}(212500\times \frac{15}{100x})$$

Express 212500\times \frac{15}{100x} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{212500\times 15}{100x})$$

Cancel out 100 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{15\times 2125}{x})$$

Multiply 15 and 2125 to get 31875.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{31875}{x})$$

The derivative of ax^{n} is nax^{n-1}.

$$-31875x^{-1-1}$$

Subtract 1 from -1.

$$-31875x^{-2}$$