Solve (1)3a^2b/6ab

$$( 1 ) \frac { 3 a ^ { 2 } b } { 6 a b }$$

Evaluate

$$\frac{a}{2}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{3^{1}a^{2}b^{1}}{6^{1}a^{1}b^{1}}$$

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

$$\frac{3^{1}}{6^{1}}a^{2-1}b^{1-1}$$

Subtract 1 from 2.

$$\frac{3^{1}}{6^{1}}a^{1}b^{1-1}$$

Subtract 1 from 1.

$$\frac{3^{1}}{6^{1}}ab^{0}$$

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

$$\frac{3^{1}}{6^{1}}a$$

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$\frac{1}{2}a$$

Differentiate w.r.t. a

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

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{3b}{6b}a^{2-1})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$\frac{1}{2}a^{0}$$

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

$$\frac{1}{2}\times 1$$

For any term t, t\times 1=t and 1t=t.

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