Differentiate Log (1 + X2) W.R.T. Tan-1 (X) - Mathematics and Statistics

Question

Differentiate
log (1 + x²) w.r.t. tan^-1(x)

Sum

Solution

Let u = log(1 + x²) and v = tan^-1 (x)

Deffrentiating both sides with respect to x.

$\frac{d u}{d x} = \frac{1}{1 + x^{2}} . 2 x, \frac{d v}{d x} = \frac{1}{1 + x^{2}}$

$\frac{d u}{d v} = \frac{\frac{d u}{d x}}{\frac{d v}{d x}} = \frac{(2 \frac{x}{1} + x^{2})}{(\frac{1}{1 + x^{2}})}$

$\frac{d u}{d v} = 2 x$

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Differentiate Log (1 + X2) W.R.T. Tan-1 (X) - Mathematics and Statistics

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