The primitive of the function `f(x)=(1-1/(x^2))a^(x+1/x)\ ,\ a >0` is `(a^(x+1/x))/((log)_e a)` (b) `(log)_e adota^(x+1/x)` (c) `(a^(x+1/x))/x(log)_e a` (d) `x(a^(x+1/x))/((log)_e a)`

The primitive of the function f(x)=(1-1/(x^2))a^(x+1/x)\ ,\ a >0 is (a) (a^(x+1/x))/((log)_e a) (b) (log)_e adota^(x+1/x) (c) (a^(x+1/x))/x(log)_e a (d) x(a^(x+1/x))/((log)_e a)

The primitive of the function f(x)=(1-(1)/(x^(2)))a^(x+(1)/(x)),a>0 is (a^(x+(1)/(x)))/((log)_(e)a) (b) (log_(e)adot a^(x+(1)/(x))(c)(a^(x+(1)/(x)))/(x)(log)_(e)a(d)x(a^(x+(1)/(x)))/((log)_(e)a)

Domain of the function f (x)= (x)/(log _(e) (1+x)) is-

Range of the function f(x)=cos((ln(x^(2)+e))/(x^(2)+1))+sin(((ln(x^(2)+e))/(x^(2)+1))

For all x in (0,1) (a) e^x (b) (log)_e (1+x) (c) sin x > x (d) (log)_e x > x

For all x in (0,1) (a) e^x (b) (log)_e (x+1) (c) sinx>x (d) (log)_e x > x

The differential coefficient of f((log)_e x) with respect to x , where f(x)=(log)_e x , is (a) x/((log)_e x) (b) 1/x(log)_e x (c) 1/(x(log)_e x) (d) none of these

The differential coefficient of f((log)_e x) with respect to x , where f(x)=(log)_e x , is (a) x/((log)_e x) (b) 1/x(log)_e x (c) 1/(x(log)_e x) (d) none of these

The differential coefficient of f((log)_e x) with respect to x , where f(x)=(log)_e x , is (a) x/((log)_e x) (b) 1/x(log)_e x (c) 1/(x(log)_e x) (d) none of these

If the primitive of (1)/((e^(x)-1)^(2)) is f(x)-log g(x)+c then