Solve 2/1,4*7/x?

$$\frac { 2 } { 1,4 } \times \frac { 7 } { x ? }$$

Evaluate

$$\frac{10}{x}$$

Solution Steps

Expand \frac{2}{1,4} by multiplying both numerator and the denominator by 10.

$$\frac{20}{14}\times \frac{7}{x}$$

Reduce the fraction \frac{20}{14} to lowest terms by extracting and canceling out 2.

$$\frac{10}{7}\times \frac{7}{x}$$

Multiply \frac{10}{7} times \frac{7}{x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{10\times 7}{7x}$$

Cancel out 7 in both numerator and denominator.

$$\frac{10}{x}$$

Differentiate w.r.t. x

$$-\frac{10}{x^{2}}$$

Steps Using Definition of a Derivative

Expand \frac{2}{1,4} by multiplying both numerator and the denominator by 10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{20}{14}\times \frac{7}{x})$$

Reduce the fraction \frac{20}{14} to lowest terms by extracting and canceling out 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{10}{7}\times \frac{7}{x})$$

Multiply \frac{10}{7} times \frac{7}{x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{10\times 7}{7x})$$

Cancel out 7 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{10}{x})$$

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

$$-10x^{-1-1}$$

Subtract 1 from -1.

$$-10x^{-2}$$