Solve frac{8a^{2}b^{4}c^-3}{a^-3b^4c^6}

$$\frac { 8 a ^ { 2 } b ^ { 4 } c ^ { - 3 } } { a ^ { - 3 } b ^ { 4 } c ^ { 6 } }$$

Evaluate

$$\frac{8a^{5}}{c^{9}}$$

Solution Steps

Cancel out b^{4} in both numerator and denominator.

$$\frac{8c^{-3}a^{2}}{a^{-3}c^{6}}$$

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

$$\frac{8c^{-3}a^{5}}{c^{6}}$$

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

$$\frac{8a^{5}}{c^{9}}$$

Differentiate w.r.t. a

$$\frac{40a^{4}}{c^{9}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{8b^{4}}{c^{3}b^{4}c^{6}}a^{2-\left(-3\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{8}{c^{9}}a^{5})$$

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}.

$$5\times \frac{8}{c^{9}}a^{5-1}$$

Do the arithmetic.

$$\frac{40}{c^{9}}a^{4}$$