Solve u^-6*u^89*u/u

$$\frac { u ^ { - 6 } \cdot u ^ { 89 } \cdot u } { u }$$

Evaluate

$$u^{83}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -6 and 89 to get 83.

$$\frac{u^{83}u}{u}$$

To multiply powers of the same base, add their exponents. Add 83 and 1 to get 84.

$$\frac{u^{84}}{u}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 84 to get 83.

$$u^{83}$$

Differentiate w.r.t. u

$$83u^{82}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}u}(\frac{uu^{89}}{1}u^{-6-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}u}(u^{90}u^{-7})$$

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}.

$$-7u^{90}u^{-7-1}$$

Do the arithmetic.

$$\left(-7u^{90}\right)u^{-8}$$