Solve frac{4a^{2}b^2c^2}{-16a^3c^2}

$$\frac { 4 a ^ { 2 } b ^ { 2 } c ^ { 2 } } { - 16 a ^ { 3 } c ^ { 2 } }$$

Differentiate w.r.t. a

$$\frac{\left(\frac{b}{a}\right)^{2}}{4}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{4b^{2}c^{2}}{-16c^{2}}a^{2-3})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

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

Evaluate

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

Solution Steps

Cancel out 4a^{2}c^{2} in both numerator and denominator.

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