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# Use the quotient rule to simplify. Assume that all variables represent positive real numbers

Use the quotient rule to simiplify. Assume that all variables represent positive real numbers
4√8/x^8

### 1 Answer by Expert Tutors

Harry D. | MathematicalMarvelMathematicalMarvel
1
quotient rule: given a valid quotient expression(Call it top over bottom[top/bottom]

[(bottom)(top') - (top)(bottom')]/bottom^2
our given expression is such that
top = 81/4
bottom = x8

Substituting yields the following:
[(bottom)(top') - (top)(bottom')]/bottom^2 ===> [(x8)(d(81/4)) - (81/4)(d(x8)]/(x8)2
(Are you with me?)
what is the derivative of a constant? 0! Now the expression becomes

[0 - (81/4)(d(x8)]/(x8)2

First, what is the value of the denominator? (Multiply the exponents in that expression yields, x16.

This yields, [- (81/4)(d(x8)]/x16
Finally, what is the derivative of x8
The formula is as follows :
f(x) = XN; then f'(x) = NXN-1; applying yields ==> [- (81/4)(8x7)]/x16

doing the rest of the calculations yields(This is calculus, and I KNOW you can do this; just convince YOURSELF you can. You are taking CALCULUS; You are among the ELITE)

Adding the exponents of 8 yields : 85/4
subtracting the exponents of X yields : X-9

ANS:  - 85/4/X9