Solve frac{2a^{2}b^{-7}c^10}{6a^-3b^2c^-3}

$$\frac { 2 a ^ { 2 } b ^ { - 7 } c ^ { 10 } } { 6 a ^ { - 3 } b ^ { 2 } c ^ { - 3 } }$$

Evaluate

$$\frac{a^{5}c^{13}}{3b^{9}}$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\frac{b^{-7}a^{2}c^{10}}{3a^{-3}c^{-3}b^{2}}$$

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

$$\frac{b^{-7}a^{5}c^{13}}{3b^{2}}$$

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

$$\frac{a^{5}c^{13}}{3b^{9}}$$

Differentiate w.r.t. a

$$\frac{5a^{4}c^{13}}{3b^{9}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{2c^{10}}{b^{7}\times \frac{6b^{2}}{c^{3}}}a^{2-\left(-3\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{c^{13}}{3b^{9}}a^{5})$$

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}.

$$5\times \frac{c^{13}}{3b^{9}}a^{5-1}$$

Do the arithmetic.

$$\frac{5c^{13}}{3b^{9}}a^{4}$$