d/dx arctan (ln(x^2))
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This involves chain rule.
First find the derivative of the outer funtion and keep multiplying with the derivatives of inner functions till all the function whose function is the given composite function have been considered. Thus,
d/dx [arctan (lnx^2)]
= [1 / (1 + (lnx^2)^2)] * d/dx (2lnx) ... [because lnx^2 = 2lnx]
= [1 / (1 + (lnx^2)^2)] * (2/x)
= 2 / [x (1 + (2lnx)^2].
First find the derivative of the outer funtion and keep multiplying with the derivatives of inner functions till all the function whose function is the given composite function have been considered. Thus,
d/dx [arctan (lnx^2)]
= [1 / (1 + (lnx^2)^2)] * d/dx (2lnx) ... [because lnx^2 = 2lnx]
= [1 / (1 + (lnx^2)^2)] * (2/x)
= 2 / [x (1 + (2lnx)^2].