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Chapter 2: Q.37 (page 198)

Use the differentiation rules developed in this section to find

the derivatives of the functions

f(x)=2(1+3x2)

Short Answer

Expert verified

The derivative of the given function is12x

Step by step solution

01

Step1. Given information

The function f(x)=2(1+3x2)

We have to find out the derivatives of the given function.

02

Step2. finding the derivatives of the function

Based on the question

f(x)=2(1+3x2),wecanopentheparenthesisbymultipying2weget,=2+6x2,

Now using the differentiation rule to find the derivate of the given function , we get

ddx(2+6x2)=d(2)dx+d(6x2)dxderivativeofaconstantis0,sod(2)dx=0andd(6x2)dx=6d(x2)dx,sincederivativeofddxxn=nxn-1,foranynonzerorationalnumbernusingpowerrule=6脳2x=12xthenthederivativeofgivenfunction,ddx2(1+x2)=0+12x=12x

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