Solve a^2*b^3*a^3/a^11*b

$$\frac { a ^ { 2 } \cdot b ^ { 3 } \cdot a ^ { 3 } } { a ^ { 11 } \cdot b }$$

Evaluate

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

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{a^{5}b^{3}}{a^{11}b}$$

Cancel out ba^{5} in both numerator and denominator.

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

Differentiate w.r.t. a

$$-\frac{6b^{2}}{a^{7}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{3}b^{3}}{b}a^{2-11})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(b^{2}a^{3}a^{-9})$$

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}.

$$-9b^{2}a^{3}a^{-9-1}$$

Do the arithmetic.

$$\left(-9b^{2}a^{3}\right)a^{-10}$$