If `f(x)=((a+x)/(b+x))^(x)+cosx` find `f'(0)`.

If f(x) = |sin x - cosx| , find f' ( pi//6)

If f(x)=(x+cosx)(x-tanx)," find "f^(')(x) .

If f'(x) = a sin x + b cos x and f'(0) = 4,f(0) = 3, f((pi)/(2))= 5 , find f(x).

If f(x)=x|x| , then find f'(0).

If f'(x)=a sin x+b cos x and f'(0)=4,f(0)=3,f((pi)/(2))=5, find f(x)

Let f(x)=(x(1+a cosx)- b sin x)/(x^(3)), x ne 0 and f(0)= 1. Then values if 'a' and 'b' so that 'f' is continuos are

Sometimes functions are defined like f(x)=max{sinx,cosx} , then f(x) is splitted like f(x)={{:(cosx, x in (0,(pi)/(4)]),(sinx, x in ((pi)/(4),(pi)/(2)]):} etc. If f(x)=max{x^(2),2^(x)} ,then if x in (0,1) , f(x)=

Sometimes functions are defined like f(x)=max{sinx,cosx} , then f(x) is splitted like f(x)={{:(cosx, x in (0,(pi)/(4)]),(sinx, x in ((pi)/(4),(pi)/(2)]):} etc. If f(x)=max{x^(2),2^(x)} ,then if x in (0,1) , f(x)=

If f(x)=x+log|x|,x!=0 find f'(x)

If (d)/(dx)[f(x)]=sinx+cosx , (i) Find f(x) (ii) Write f(x) , when f(x)=1