Solve frac{a^{-4}b^{-5}c^-3}{a^7b^2c^6}

$$\frac { a ^ { - 4 } b ^ { - 5 } c ^ { - 3 } } { a ^ { 7 } b ^ { 2 } c ^ { 6 } }$$

Differentiate w.r.t. a

$$-\frac{11}{b^{7}c^{9}a^{12}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{c^{3}b^{5}b^{2}c^{6}}a^{-4-7})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{b^{7}c^{9}}a^{-11})$$

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}.

$$-11\times \frac{1}{b^{7}c^{9}}a^{-11-1}$$

Do the arithmetic.

$$\left(-\frac{11}{b^{7}c^{9}}\right)a^{-12}$$

Evaluate

$$\frac{1}{b^{7}c^{9}a^{11}}$$

Solution Steps

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

$$\frac{1}{b^{7}c^{9}a^{11}}$$