Solve (-2r^2s^2div(4rs^2)

$$( - 2 r ^ { 2 } s ^ { 2 } \div ( 4 r s ^ { 2 } )$$

Evaluate

$$-\frac{r}{2}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{\left(-2\right)^{1}r^{2}s^{2}}{4^{1}r^{1}s^{2}}$$

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

$$\frac{\left(-2\right)^{1}}{4^{1}}r^{2-1}s^{2-2}$$

Subtract 1 from 2.

$$\frac{\left(-2\right)^{1}}{4^{1}}r^{1}s^{2-2}$$

Subtract 2 from 2.

$$\frac{\left(-2\right)^{1}}{4^{1}}rs^{0}$$

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

$$\frac{\left(-2\right)^{1}}{4^{1}}r$$

Reduce the fraction \frac{-2}{4} to lowest terms by extracting and canceling out 2.

$$-\frac{1}{2}r$$

Differentiate w.r.t. r

$$-\frac{1}{2} = -0.5$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}r}(\left(-\frac{2s^{2}}{4s^{2}}\right)r^{2-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}r}(-\frac{1}{2}r^{1})$$

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}.

$$-\frac{1}{2}r^{1-1}$$

Do the arithmetic.

$$-\frac{1}{2}r^{0}$$

For any term t except 0, t^{0}=1.

$$-\frac{1}{2}$$