For `x in x != 0, if y(x)` differential function such that `x int_1^x y(t)dt=(x+1)int_1^x t y(t)dt,` then `y(x)` equals: (where C is a constant.)

Let f:RtoR be a differentiable function such that f(x)=x^(2)+int_(0)^(x)e^(-t)f(x-t)dt . f(x) increases for

Let f:[1,oo) to [2,oo) be a differentiable function such that f(1)=2. If 6int_1^xf(t)dt=3xf(x)-x^3 for all xgeq1, then the value of f(2) is

A function satisfying int_0^1f(tx)dt=nf(x) , where x>0 is

Differentiate a^(x) w.r.t x, where a is a positive constant

Let f be differentiable function satisfying f((x)/(y))=f(x) - f(y)"for all" x, y gt 0 . If f'(1) = 1, then f(x) is

Differentiate w.r.t x the function (log x)^(log x), x gt 1

Differentiate the following functions with respect to x. y= (sin x)^(x)+ ((1)/(x))^(cos x)

Let f : (0, oo) rarr R be a continuous function such that f(x) = int_(0)^(x) t f(t) dt . If f(x^(2)) = x^(4) + x^(5) , then sum_(r = 1)^(12) f(r^(2)) , is equal to

Let y = f(x) be a differentiable function, AA x in R and satisfies, f(x) = x+ int_(0)^(1)x^(2)z f(z) dz + int_(0)^(1)x z^(2) f(z) dz , then