   Chapter 2.5, Problem 26E

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Textbook Problem
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# Find the derivative of the function. f ( t ) = t t 2 + 4

To determine

To find: The derivative of a function

Explanation

Rules:

a) Quotient rule: ddxfxgx=gxddxfx-fxddx(gx)gx2

b) Chain rule: If Fx=fogx=fgx then F'x=f'gx*g'x

c) Power rule : ddxxn=nxn-1

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

e) Constant function rule: ddxC=0

Given:

ft=tt2+4

Calculation:

Rewrite equation as

ft=tt2+412

Differentiate given function with respect to t,

f't=ddttt2+412

By using power rule and chain rule,

f't=12tt2+4-12ddt(tt2+4)

By using quotient rule,

f't=12tt2+4-12t2+4ddtt-tddtt2+4t2+42

By using sum rule,

f't

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