   Chapter 2.2, Problem 24E

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# Find the derivative of the function using the definition of derivative. State the domain of the function and the domain of its derivative. g ( t ) = 1 t

To determine

To find: the derivative of the function by using the definition of derivative. State the domain of function and domain of derivative of its function.

Explanation

Definition of derivative is

f'x= limh0 fx+h-f(x)h

Here gt=1t

Therefore, gt+h=1t+h

By using this values in the formula

g't= limh0 1t+h-1th

g't=limh0 (t- t+h)/ tt+hh

g't=limh0 (t- t+h)h(tt+h)

To rationalise the numerator, multiply numerator and denominator by t+ t+h

g't=limh0 t- t+h(t+ t+hh(tt+h)  (t+ t+h)

By using the identity (a – b)(a + b) = a2 – b2, numerator becomes

t- t+h(t+ t+h)  =t2-t+h2=t-t+

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