4.i) If `f(x)=7^(x^(3)+3x)(x>0)` ,then find `f'(x)`.

If f(x)= {4 - (x-7)^(3)} , then find f^(-1)(x)=

If f(x)=x^(3)-(1)/(x^(3)) , then find the value of f(x)+f(-x) .

If f(x)=2x^(3)-13x^(2)+17x+12 Then find (i)" "f(2)(ii) " "f(-3)(iii)" "f(0)

If f^(prime)(x)=3x^2-2/(x^3) and f(1)=0 , find f(x) .

If f(x)=7x^(4)-2x^(3)-8x-5 find f(-1)

Let f:RtoR be a differntiable function satisfying f(x)=x^(2)+3int_(0)^(x)e^(-t^(3)).f(x-t^(3))dt . Then find f(x) .

If f: R^+ to R , f(x) + 3x f(1/x)= 2(x+1),t h e n find f(x)

If a function 'f' satisfies the relation f(x)f^('')(x)-f(x)f^(')(x) -f^(')(x)^(2)=0 AA x in R and f(0)=1=f^(')(0) . Then find f(x) .

If f(x) = [4-(x-7)^(3)], then f^(-1)(x)= ………… .

If f(x)=x^3+7x^2+8x-9 , find f\ '\ (4) .