Solve 25uv/40u^4v

$$\frac { 25 u v } { 40 u ^ { 4 } v }$$

Evaluate

$$\frac{5}{8u^{3}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{25^{1}u^{1}v^{1}}{40^{1}u^{4}v^{1}}$$

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

$$\frac{25^{1}}{40^{1}}u^{1-4}v^{1-1}$$

Subtract 4 from 1.

$$\frac{25^{1}}{40^{1}}u^{-3}v^{1-1}$$

Subtract 1 from 1.

$$\frac{25^{1}}{40^{1}}\times \frac{1}{u^{3}}v^{0}$$

For any number a except 0, a^{0}=1.

$$\frac{25^{1}}{40^{1}}\times \frac{1}{u^{3}}$$

Reduce the fraction \frac{25}{40} to lowest terms by extracting and canceling out 5.

$$\frac{5}{8}\times \frac{1}{u^{3}}$$

Differentiate w.r.t. u

$$-\frac{15}{8u^{4}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}u}(\frac{25v}{40v}u^{1-4})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}u}(\frac{5}{8}u^{-3})$$

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}.

$$-3\times \frac{5}{8}u^{-3-1}$$

Do the arithmetic.

$$-\frac{15}{8}u^{-4}$$