Solve (8a^{2}b^{3}c^2)div(4a^4b^3c^2)

$$( 8 a ^ { 2 } b ^ { 3 } c ^ { 2 } ) \div ( 4 a ^ { 4 } b ^ { 3 } c ^ { 2 } )$$

Differentiate w.r.t. a

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

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{8c^{2}b^{3}}{4c^{2}b^{3}}a^{2-4})$$

Do the arithmetic.

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

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}.

$$-2\times 2a^{-2-1}$$

Do the arithmetic.

$$-4a^{-3}$$

Evaluate

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

Solution Steps

Cancel out 4a^{2}c^{2}b^{3} in both numerator and denominator.

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