Solve ab^2c^4/a^2

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

Differentiate w.r.t. a

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

Solution Steps

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

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

Do the arithmetic.

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

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}.

$$-b^{2}c^{4}a^{-1-1}$$

Do the arithmetic.

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

Evaluate

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

Solution Steps

Cancel out a in both numerator and denominator.

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