Solve (-1/4ab^2)3div(-0.5a^2b)=

$$( - \frac { 1 } { 4 } a b ^ { 2 } ) 3 \div ( - 0.5 a ^ { 2 } b ) =$$

Evaluate

$$\frac{3b}{2a}$$

Solution Steps

Cancel out ab in both numerator and denominator.

$$\frac{-\frac{1}{4}\times 3b}{-0.5a}$$

Multiply -\frac{1}{4} and 3 to get -\frac{3}{4}.

$$\frac{-\frac{3}{4}b}{-0.5a}$$

Differentiate w.r.t. a

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

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\left(-\frac{\frac{3b^{2}}{4}}{-\frac{b}{2}}\right)a^{1-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{3b}{2}\times \frac{1}{a})$$

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}.

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

Do the arithmetic.

$$\left(-\frac{3b}{2}\right)a^{-2}$$