Solve 1875u^4y^10/45u^2y^2

$$\frac { 1875 u ^ { 4 } y ^ { 10 } } { 45 u ^ { 2 } y ^ { 2 } }$$

Evaluate

$$\frac{125u^{2}y^{8}}{3}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{1875^{1}u^{4}y^{10}}{45^{1}u^{2}y^{2}}$$

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

$$\frac{1875^{1}}{45^{1}}u^{4-2}y^{10-2}$$

Subtract 2 from 4.

$$\frac{1875^{1}}{45^{1}}u^{2}y^{10-2}$$

Subtract 2 from 10.

$$\frac{1875^{1}}{45^{1}}u^{2}y^{8}$$

Reduce the fraction \frac{1875}{45} to lowest terms by extracting and canceling out 15.

$$\frac{125}{3}u^{2}y^{8}$$

Differentiate w.r.t. u

$$\frac{250uy^{8}}{3}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}u}(\frac{1875y^{10}}{45y^{2}}u^{4-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}u}(\frac{125y^{8}}{3}u^{2})$$

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}.

$$2\times \frac{125y^{8}}{3}u^{2-1}$$

Do the arithmetic.

$$\frac{250y^{8}}{3}u^{1}$$

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

$$\frac{250y^{8}}{3}u$$