For a differentiable positive function f(x), if f(x)-etan ' x ▽ X E R and y-mx +c is a tangent to f(x) at (x1.yi) where x,e(α'β), then-

Let f : R rarr R be a differentiable function satisfying f(x) = f(y) f(x - y), AA x, y in R and f'(0) = int_(0)^(4) {2x}dx , where {.} denotes the fractional part function and f'(-3) - alpha e^(beta) . Then, |alpha + beta| is equal to.......

Let f : R rarr R be a differentiable function satisfying f(x) = f(y) f(x - y), AA x, y in R and f'(0) = int_(0)^(4) {2x}dx , where {.} denotes the fractional part function and f'(-3) = alpha e^(beta) . Then, |alpha + beta| is equal to.......

A function f(x) is differentiable at x=c(c in R). Let g(x)=|f(x)|,f(c)=0 then

The differential coefficient of f(log_e x) w.r.t. x, where f(x) = log_e x, is

The differential coefficient of f(log_e x) w.r.t. x, where f(x) = log_e x, is