   Chapter 2.5, Problem 22E

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# Find the derivative of the function. y = ( x + 1 x ) 5

To determine

To find:

Derivative of the function

Explanation

Rules:

a) Constant function rule: d(C)dx=0

b) Power function rule: d(xn)dx=nxn-1

c) Constant multiple rule: d(Cf(x))dx=Cd(f(x))dx

d) Sum rule: d(fx+g(x))dx=d(f(x))dx+d(g(x))dx

Given:

y=x+1x5

Calculation:

y=x+1x5

Rewrite equation,

y=x+x-15

Express y=fogx=fgx where y=fu= u5 and u=gx=x+x-1

Since,

f'u=dfdu=du5du

By power function rule,

f'(u)=5u4

Now,

g'x=ddxx+x-1

By sum rule,

g'(x)=ddxx+ddxx-1

By power function rule,

g'&#

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