Solve 33a^-2b^2/44a^2b^-2

$$\frac { 33 a ^ { - 2 } b ^ { 2 } } { 44 a ^ { 2 } b ^ { - 2 } }$$

Evaluate

$$\frac{3\times \left(\frac{b}{a}\right)^{4}}{4}$$

Solution Steps

Cancel out 11 in both numerator and denominator.

$$\frac{3a^{-2}b^{2}}{4b^{-2}a^{2}}$$

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

$$\frac{3a^{-2}b^{4}}{4a^{2}}$$

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

$$\frac{3b^{4}}{4a^{4}}$$

Differentiate w.r.t. a

$$-\frac{3b^{4}}{a^{5}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{33b^{2}b^{2}}{44}a^{-2-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{3b^{4}}{4}a^{-4})$$

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}.

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

Do the arithmetic.

$$\left(-3b^{4}\right)a^{-5}$$