Solve 24c^5d^3/16c^-5d^20

$$\frac { 24 c ^ { 5 } d ^ { 3 } } { 16 c ^ { - 5 } d ^ { 20 } }$$

Evaluate

$$\frac{3c^{10}}{2d^{17}}$$

Solution Steps

Cancel out 8d^{3} in both numerator and denominator.

$$\frac{3c^{5}}{2c^{-5}d^{17}}$$

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

$$\frac{3c^{10}}{2d^{17}}$$

Differentiate w.r.t. c

$$\frac{15c^{9}}{d^{17}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}c}(\frac{24d^{3}}{16d^{20}}c^{5-\left(-5\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}c}(\frac{3}{2d^{17}}c^{10})$$

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}.

$$10\times \frac{3}{2d^{17}}c^{10-1}$$

Do the arithmetic.

$$\frac{15}{d^{17}}c^{9}$$