Can u plzz expain me the second step of illustration 2..

Can u plzz expain me the second step of illustration 2.. ILLUSTRATION If f(x) f' (0) is Ans. (b) SOLUTION we have, f (X) = erg(X) -erg(O, g (O) -2. g' (O - ILLUSTRATION 2 Let f (x) (ax + b) cos x + (cx + d) sin x and (x) x cos x for all x. Then, (d) none of these Ans. (a) sow-no,N We have, f(x) (ax + b) cos x + (cx + d) sin x f' (x) = — (ax + b) sin x + acosx+ (cx x f' (x) = (cx But, f' (x) = x cos x for all x. (cx+d + a) cos x + (c — ax — b) sin x = x cos x for all x c = 0, a O and c —b z 0 LLUSTRATION 3 tan-I x, then f' (1) is equal to (C) -A-lt [CEE (Delhi) 2C DLUTION We have, f (x) = x tan-I x f' (x) = tan¯lx+ x

Dear student

We have,f(x)=ax+bcosx+cx+dsinxApplying chain rule, we getf'(x)=(ax+b)×ddxcosx+cosx×ddxax+b+cx+d×ddxsinx+sinx×ddxcx+df'(x)=-sinxax+b+acosx+cosx(cx+d)+csinx
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In second step Mr.RD Sharma took diffrenciation of the function by applying simple chain rule i.e diffrentiating the main function HERE sinx and cosx later diff. the inner bracket function which is (ax+b) which gives out x so this is what done in 2nd step.
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Ty
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