Solve w*w^-31/w^-58

$$\frac { w \cdot w ^ { - 31 } } { w ^ { - 58 } }$$

Evaluate

$$w^{28}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and -31 to get -30.

$$\frac{w^{-30}}{w^{-58}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -58 from -30 to get 28.

$$w^{28}$$

Differentiate w.r.t. w

$$28w^{27}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}w}(\frac{w}{1}w^{-31-\left(-58\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}w}(ww^{27})$$

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}.

$$27ww^{27-1}$$

Do the arithmetic.

$$27ww^{26}$$