   Chapter 2.3, Problem 62E

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# Find the first and second derivatives of the function. f ( x ) = 1 3 − x

To determine

To find: First and second derivative of the function.

Explanation

1) Concept:

By differentiating first function we can obtain first derivative and differentiating the first derivative thus obtained will give second derivative.

2) Formula:

Let f and g are differentiable functions then

i. Quotient rule: ddxfxgx=gx.ddxfx-fxddx[gx]gx2

iii. Power rule:  ddxxn=nxn-1

iv. Derivative of constant multiple: ddx kfx=kddxfx

v. Derivative of constant: ddxk=0 where k is constant.

3) Given: fx=13 -x

4) Calculations:

Differentiating given function with respect to x,

By using quotient rule,

f'x=ddx13 -x=3 -x.ddx1-1ddx3-x3 -x2

=3 -x.ddx1-ddx3-ddxx3 -x2

By using rules power and constant rules rule,

=3 -x

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