Solve s/s^-34*s^62*s^0

$$\frac { s } { s ^ { - 34 } \cdot s ^ { 62 } \cdot s ^ { 0 } }$$

Evaluate

$$\frac{1}{s^{27}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -34 and 62 to get 28.

$$\frac{s}{s^{28}s^{0}}$$

To multiply powers of the same base, add their exponents. Add 28 and 0 to get 28.

$$\frac{s}{s^{28}}$$

Rewrite s^{28} as ss^{27}. Cancel out s in both numerator and denominator.

$$\frac{1}{s^{27}}$$

Differentiate w.r.t. s

$$-\frac{27}{s^{28}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}s}(\frac{1}{s^{0}s^{62}}s^{1-\left(-34\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}s}(\frac{1}{s^{62}}s^{35})$$

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}.

$$35\times \frac{1}{s^{62}}s^{35-1}$$

Do the arithmetic.

$$\frac{35}{s^{62}}s^{34}$$