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Differentiate following.
Solution :It requires the product rule & each derivative in the product rule will need a chain rule application as well.
T ′ ( x ) =1/1+(2x)2 (2) (1-3x2)(1/3) +tan-1(2x)(1/3)(1-3x2)(-2/3)(-6x)
= 2(1 - 3x2 )(1/3) /(1+(2x)2 - 2(1 - 3x2 )-(2/3) tan -1 ( 2x )
We know that,
d (tan -1 x ) / dx = (1/(1+x2)
While doing the chain rule with this we remember that we've got to leave the inside function
alone. That means that where we have the x2 in the derivative of tan -1 x we will have to have (inside function )2 .
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