Question

Differenciate with respect to x and Check it is write or wrong f(x) = Sinx + Cosx + logx?​

Answer 1

Differentiating with respect to X we get

f'(x) = cosx - sinx + 1/x

we know that intigration is the reverse of differentiation so

$\int( \sin(x) + \cos(x) + log(x) )dx$

on intigration we get

- cosx + sinx + 1/x + c

Which is equal to f(x)

Answer 2

$f(x) = \sin(x) + \cos(x) + ln(x) \\ differentiating \: wrt \: x \\ f'(x) = \cos(x) - \sin(x) + \frac{1}{x} \\ integrating \: f'(x),\: we\: get\\</p><p>F(x)=\int f(x)\\</p><p>\intf(x)=-\cos(x)+\sin(x)+(xln(x)-x)$