`f(x) ` is the integral of `(2sinx-sin2x)/(x^3),x!=0.` Find `lim_(x->0)f^(prime)(x)[w h e r ef^(prime)(x)=(df)/(dx)]`

f(x) is the integral of (2sin x-sin2x)/(x^(3)),x!=0. Find lim_(x rarr0)f'(x)[wheref'(x)=(df)/(dx)]

If f(x) is the integral of (2 sin x-sin 2 x)/(x^(3)), "where x" ne 0, "then find" lim_(x rarr 0) f'(x) .

If f(x) is the integral of (2 sin x-sin 2 x)/(x^(3)), "where x" ne 0, "then find" lim_(x rarr 0) f'(x) .

If f(x) is the integral of (2 sin x-sin 2 x)/(x^(3)), "where x" ne 0, "then find" underset(x rarr 0)("lim")f'(x) .

If f(x)=int((2sin x-sin2x)/(x^(3))dx);x!=0 then lim_(x rarr0)f'(x) is: (A) 0(B)oo(C)-1 (D) 1

If f(x)=|logx|,xgt0 ,find f^(prime)(1/e)a n df^(prime)(e)

A function f: R->R satisfies that equation f(x+y)=f(x)f(y) for all x ,\ y in R , f(x)!=0 . Suppose that the function f(x) is differentiable at x=0 and f^(prime)(0)=2 . Prove that f^(prime)(x)=2\ f(x) .

A function f: R->R satisfies that equation f(x+y)=f(x)f(y) for all x ,\ y in R , f(x)!=0 . Suppose that the function f(x) is differentiable at x=0 and f^(prime)(0)=2 . Prove that f^(prime)(x)=2\ f(x) .

Suppose that f(x) isa quadratic expresson positive for all real xdot If g(x)=f(x)+f^(prime)(x)+f^(x), then for any real x(w h e r ef^(prime)(x)a n df^(x) represent 1st and 2nd derivative, respectively). g(x) 0 c. g(x)=0 d. g(x)geq0