Solve 14B^3/21B

$$\frac { 14 B ^ { 3 } } { 21 B }$$

Evaluate

$$\frac{2B^{2}}{3}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{14^{1}B^{3}}{21^{1}B^{1}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{14^{1}B^{3-1}}{21^{1}}$$

Subtract 1 from 3.

$$\frac{14^{1}B^{2}}{21^{1}}$$

Reduce the fraction \frac{14}{21} to lowest terms by extracting and canceling out 7.

$$\frac{2}{3}B^{2}$$

Differentiate w.r.t. B

$$\frac{4B}{3}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}B}(\frac{14}{21}B^{3-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}B}(\frac{2}{3}B^{2})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$2\times \frac{2}{3}B^{2-1}$$

Do the arithmetic.

$$\frac{4}{3}B^{1}$$

For any term t, t^{1}=t.

$$\frac{4}{3}B$$