Let y = xx cos x + \(\cfrac{\text x^2+1}{\text x^2+1}\)
⇒ y = a + b
where a = xx cos x ; b = \(\cfrac{\text x^2+1}{\text x^2+1}\)
{ Using chain rule, \(\cfrac{d(u +a)}{d\text x}=\cfrac{du}{d\text x}+\cfrac{da}{d\text x}\) where a and u are any variables }
a = xx cos x
Taking log both the sides:
⇒ log a = log xx cos x
⇒ log a = x cos x log x
{log xa = a log x}
Differentiating with respect to x:
{ Using chain rule, \(\cfrac{d(u +a)}{d\text x}=\cfrac{du}{d\text x}+\cfrac{da}{d\text x}\) where a and u are any variables }