Solve 14x^2b^4/21x^6b^3

$$\frac { 14 x ^ { 2 } b ^ { 4 } } { 21 x ^ { 6 } b ^ { 3 } }$$

Evaluate

$$\frac{2b}{3x^{4}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{14^{1}x^{2}b^{4}}{21^{1}x^{6}b^{3}}$$

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

$$\frac{14^{1}}{21^{1}}x^{2-6}b^{4-3}$$

Subtract 6 from 2.

$$\frac{14^{1}}{21^{1}}x^{-4}b^{4-3}$$

Subtract 3 from 4.

$$\frac{14^{1}}{21^{1}}\times \frac{1}{x^{4}}b^{1}$$

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

$$\frac{2}{3}\times \frac{1}{x^{4}}b$$

Differentiate w.r.t. x

$$-\frac{8b}{3x^{5}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{14b^{4}}{21b^{3}}x^{2-6})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2b}{3}x^{-4})$$

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}.

$$-4\times \frac{2b}{3}x^{-4-1}$$

Do the arithmetic.

$$\left(-\frac{8b}{3}\right)x^{-5}$$