Solve frac{210ab^{4}c^2}{-30a^4b^2c^3}

$$\frac { 210 a b ^ { 4 } c ^ { 2 } } { - 30 a ^ { 4 } b ^ { 2 } c ^ { 3 } }$$

Evaluate

$$-\frac{7b^{2}}{ca^{3}}$$

Solution Steps

Cancel out 30ab^{2}c^{2} in both numerator and denominator.

$$\frac{7b^{2}}{-ca^{3}}$$

Cancel out -1 in both numerator and denominator.

$$\frac{-7b^{2}}{ca^{3}}$$

Differentiate w.r.t. a

$$\frac{21b^{2}}{ca^{4}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{210c^{2}b^{4}}{-30b^{2}c^{3}}a^{1-4})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\left(-\frac{7b^{2}}{c}\right)a^{-3})$$

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}.

$$-3\left(-\frac{7b^{2}}{c}\right)a^{-3-1}$$

Do the arithmetic.

$$\frac{21b^{2}}{c}a^{-4}$$