Solve s^9/s*s*s^-4

$$\frac { s ^ { 9 } } { s \cdot s \cdot s ^ { - 4 } }$$

Evaluate

$$s^{11}$$

Solution Steps

Multiply s and s to get s^{2}.

$$\frac{s^{9}}{s^{2}s^{-4}}$$

To multiply powers of the same base, add their exponents. Add 2 and -4 to get -2.

$$\frac{s^{9}}{s^{-2}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -2 from 9 to get 11.

$$s^{11}$$

Differentiate w.r.t. s

$$11s^{10}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}s}(\frac{s^{4}}{s}s^{9-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}s}(s^{3}s^{8})$$

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}.

$$8s^{3}s^{8-1}$$

Do the arithmetic.

$$8s^{3}s^{7}$$