For `f(x)` find such an antiderivative which attains the given magnitude `y = y_0` at `x=x_0`.

If f(x-y)=f(x).g(y)-f(y).g(x) and g(x-y)=g(x).g(y)+f(x).f(y) for all x in R. If right handed derivative at x=0 exists for f(x) find the derivative of g(x) at x=0

Find the antiderivative of f(x) given by f'(x)=4x^(3)-(3)/(x^(4)) such that f(2)=0 .

If f(x-y)=f(x).g(y)-f(y).g(x) and g(x-y)=g(x).g(y)+f(x).f(y) for all x in R . If right handed derivative at x=0 exists for f(x) find the derivative of g(x) at x =0

If f(x-y)=f(x).g(y)-f(y).g(x) and g(x-y)=g(x).g(y)+f(x).f(y) for all x in R . If right handed derivative at x=0 exists for f(x) find the derivative of g(x) at x =0

If f(x-y)=f(x).g(y)-f(y).g(x) and g(x-y)=g(x).g(y)+f(x).f(y) for all x in R . If right handed derivative at x=0 exists for f(x) find the derivative of g(x) at x =0

If f(x-y)=f(x).g(y)-f(y).g(x) and g(x-y)=g(x).g(y)+f(x).f(y) for all x in R . If right handed derivative at x=0 exists for f(x) find the derivative of g(x) at x =0

Find the circumcentre of the triangle whose sides are given by x+y=0, 2x+y+5=0 and x-y=0

Find the antiderivative F of f defined by f(x)=4 x^3-6 , where F(0)=3

If f(x) = (1)/(cos^(2)xsqrt(1+tanx)) then its antiderivative F(x) (given that F(0) = (4) is