   Chapter 2.3, Problem 22E

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# Differentiate the function. D ( t ) = 1 + 16 t 2 ( 4 t ) 3

To determine

To differentiate:  The function Dt=1+16t24t3

Explanation

Concept:

To differentiate given function, we may use rules of differentiation and also may convert radicals into exponent form if necessary.

Formula:

(i) Power rule:  ddxxn=nxn-1

(ii) Rule of exponent: xnxm=xm-n.

(iii) The addition rule, if f  and g are both differentiable,

Then  ddxfx+gx=ddxfx+ddxg(x)

Given:

Dt=1+16t24t3

Calculations:

We have Dt=1+16t24t3

By simplifying and using rule of exponents, Dt can be written as,

Dt=1+16t24t3=1+16t264t3=164t3+16t264t3=t-364+t-14

Differentiating with respect to t,

By using Addition rule of differentiation,

ddxfx+gx=ddxfx+ ddxgx

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