Solve 16x^2/7:4x^3/21

$$\frac { 16 x ^ { 2 } } { 7 } : \frac { 4 x ^ { 3 } } { 21 }$$

Evaluate

$$\frac{12}{x}$$

Solution Steps

Divide \frac{16x^{2}}{7} by \frac{4x^{3}}{21} by multiplying \frac{16x^{2}}{7} by the reciprocal of \frac{4x^{3}}{21}.

$$\frac{16x^{2}\times 21}{7\times 4x^{3}}$$

Cancel out 4\times 7x^{2} in both numerator and denominator.

$$\frac{3\times 4}{x}$$

Multiply 3 and 4 to get 12.

$$\frac{12}{x}$$

Differentiate w.r.t. x

$$-\frac{12}{x^{2}}$$

Steps Using Definition of a Derivative

Divide \frac{16x^{2}}{7} by \frac{4x^{3}}{21} by multiplying \frac{16x^{2}}{7} by the reciprocal of \frac{4x^{3}}{21}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{16x^{2}\times 21}{7\times 4x^{3}})$$

Cancel out 4\times 7x^{2} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3\times 4}{x})$$

Multiply 3 and 4 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{12}{x})$$

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

$$-12x^{-1-1}$$

Subtract 1 from -1.

$$-12x^{-2}$$