Solve ks/2k^4s^6

$$\frac { ks } { 2 k ^ { 4 } s ^ { 6 } }$$

Differentiate w.r.t. s

$$-\frac{5}{2k^{3}s^{6}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}s}(\frac{k}{2k^{4}}s^{1-6})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}s}(\frac{1}{2k^{3}}s^{-5})$$

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}.

$$-5\times \frac{1}{2k^{3}}s^{-5-1}$$

Do the arithmetic.

$$\left(-\frac{5}{2k^{3}}\right)s^{-6}$$

Evaluate

$$\frac{1}{2k^{3}s^{5}}$$

Solution Steps

Cancel out ks in both numerator and denominator.

$$\frac{1}{2k^{3}s^{5}}$$