If `f(x)=|x-2|a n dg(x)=f[f(x)],t h e ng^(prime)(x)=` ______ for x>2

If f(x)=(x+1)/(x-1)a n dg(x)=1/(x-2),t h e n discuss the continuity of f(x),g(x),a n dfog(x)dot

If f^(prime)(x)=sqrt(2x^2-1)a n dy=f(x^2),t h e n(dy)/(dx)a tx=1 is 2 (b) 1 (c) -2 (d) none of these

If for a continuous function f,f(0)=f(1)=0,f^(prime)(1)=2a n dy(x)=f(e^x)e^(f(x)) , then y^(prime)(0) is equal to a. 1 b. 2 c. 0 d. none of these

Evaluate: ifintg(x)dx=g(x),t h e nintg(x){f(x)+f^(prime)(x)}dx

If the function f(x)=-4e^((1-x)/2)+1+x+(x^2)/2+(x^3)/3a n dg(x)=f^(-1)(x), then the reciprocal of g^(prime)((-7)/6) is_________

If f''(x)=-f(x)a n dg(x)=f^(prime)(x) and F(x)=(f(x/2))^2+(g(x/2))^2 and given that F(5)=5, then F(10) is (a)5 (b) 10 (c) 0 (d) 15

If f(x)=log((1+x)/(1-x)),t h e n (a) f(x_1)f(x)=f(x_1+x_2) (b) f(x+2)-2f(x+1)+f(x)=0 (c) f(x)+f(x+1)=f(x^2+x) (d) f(x_1)+f(x_2)=f((x_1+x_2)/(1+x_1x_2))

If f(x)=x|x|, then prove that f^(prime)(x)=2|x|

Which of the following functions are identical? f(x)=1nx^2a n dg(x)=21nx f(x)=(log)_x ea n dg(x)=1/((log)_e x) f(x)="sin"(cos^(-1)x)a n dg(x)="cos"(sin^(-1)x) non eoft h e s e

If y=f(x^3),z=g(x^5),f^(prime)(x)=tanx ,a n dg^(prime)(x)=secx , then find the value of (lim)_(xvec0)(((dy)/(dz)))/x