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Find the derivatives of each of the functions in Exercises 17–50. In some cases it may be convenient to do some preliminary algebra

f(x)=x2arctanx2

Short Answer

Expert verified

The derivative is2xarctanx2+x22x1+x4.

Step by step solution

01

Step 1. Given Information.

The given function isf(x)=x2arctanx2.

02

Step 2. Preliminary Algebra.

It is known,

(fg)'(x)=f'(x)g(x)+f(x)g'(x)(fu)'(x)=f'(u(x))u'(x)ddxtan-1x=11+x2

03

Step 3. Derivative of the function.

The derivative of the function will be,


ddxx2arctanx2=ddxx2arctanx2+x2ddxarctanx2=2xarctanx2+x211+x22ddxx22xarctanx2+x22x1+x4

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