If `f(1-x)=f(x)` for all `x ,f^(prime)(1)=0andf^(prime)(0)` exists, find its value.

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

If f(0)=f(1)=0 , f^(prime)(1)=f^(prime)(0)=2 and y=f(e^x)e^(f(x)) , write the value of (dy)/(dx) at x=0 .

Let f(x+y)=f(x)f(y) for all x and y . Suppose f(5)=2 and f^(prime)(0)=3 , find f^(prime)(5) .

f^(prime)(x)=phi(x) and phi^(prime)(x)=f(x) for all x. Also, f(3)=5 and f^(prime)(3)=4 . Then the value of [f(10)]^2-[phi(10)]^2 is _____

f^(prime)(x)=phi(x) and phi^(prime)(x)=f(x) for all x. Also, f(3)=5 and f^(prime)(3)=4 . Then the value of [f(10)]^2-[phi(10)]^2 is _____

f^(prime)(x)=phi(x) and phi^(prime)(x)=f(x) for all x.Also,f(3)=5 and f^(prime)(3)=4 . Then the value of [f(10)]^2-[phi(10)]^2 is _____

f(x)={(a x(x-1)+b ,, x 3):} Find the values of the constants a , b , p \ a n d \ q so that all the following conditions are satisfied f(x) is continuous for all x , f^(prime)(1) does not exist and f^(prime)(x) is continuous at x=3

f(x)={(a x(x-1)+b ,, x 3):} Find the values of the constants a,b, p \ a n d \ q so that all the following conditions are satisfied f(x) is continuous for all x , f^(prime)(1) does not exist and f^(prime)(x) is continuous at x=3

If f(x)=log{(u(x))/(v(x))},\ u(1)=v(1) and u^(prime)(1)=v^(prime)(1)=2 , then find the value of f^(prime)(1) .

If f(x)=log{(u(x))/(v(x))},\ u(1)=v(1) and u^(prime)(1)=v^(prime)(1)=2 , then find the value of f^(prime)(1) .