Solve 6ab^-6/2a^-1b^-3

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

Evaluate

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

Solution Steps

Cancel out 2 in both numerator and denominator.

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

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

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

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

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

Differentiate w.r.t. a

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

Solution Steps

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

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

Do the arithmetic.

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

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}.

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

Do the arithmetic.

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

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

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