Solve 4s^0/s^-6*2s^2

$$\frac { 4 s ^ { 0 } } { s ^ { - 6 } \cdot 2 s ^ { 2 } }$$

Evaluate

$$2s^{4}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -6 and 2 to get -4.

$$\frac{4s^{0}}{s^{-4}\times 2}$$

Cancel out 2 in both numerator and denominator.

$$\frac{2s^{0}}{s^{-4}}$$

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

$$2s^{4}$$

Differentiate w.r.t. s

$$8s^{3}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -6 and 2 to get -4.

$$\frac{\mathrm{d}}{\mathrm{d}s}(\frac{4s^{0}}{s^{-4}\times 2})$$

Cancel out 2 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}s}(\frac{2s^{0}}{s^{-4}})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}s}(2s^{4})$$

The derivative of ax^{n} is nax^{n-1}.

$$4\times 2s^{4-1}$$

Multiply 4 times 2.

$$8s^{4-1}$$

Subtract 1 from 4.

$$8s^{3}$$