If `f(x)=|logx|` , `x >0` , find `f^(prime)(1//e)` and `f^(prime)(e)` .

If f(x)=|log x|,x>0, find f'((1)/(e)) andf '(e)

f(x)=log_(e)x, find value of f(1)

If F(x)=f(x)dotg(x) and f^(prime)(x)dotg^(prime)(x)=c , prove that (F")/F=f^(primeprime)/f+g^(primeprime)/g+(2c)/(fg)&F^(primeprimeprime)/F=f^(primeprimeprime)/f+g^(primeprimeprime)/g

If f(x)=|(log)_(10)x|,t h e na tx=1 a. f(x) is continuous and f^(prime)(1)=(log)_(10)e b. f(x) is continuous and f^(prime)(1)=-(log)_(10)e c. f(x) is continuous and f^(prime)(1^-)=(log)_(10)e d. f(x) is continuous and f^(prime)(1^-)=-(log)_(10)e

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) .

If f(x)=log(logx)," then "f'(e)=

If f(x)=e^(x)(x^(2)+1) then find f'(x)

A function f: R->R satisfies sinxcosy(f(2x+2y)-f(2x-2y)=cosxsiny(f(2x+2y)+f(2x-2y))dot If f^(prime)(0)=1/2,t h e n (a)f^(prime)(x)=f(x)=0 (b)4f^(x)+f(x)=0 (c)f^(x)+f(x)=0 (d)4f^(x)-f(x)=0

If f(x)=|"cos"(x+x^2)"sin"(x+x^2)-"cos"(x+x^2)"sin"(x-x^2)"cos"(x-x^2)sin(x-x^2)sin2x0sin2x^2|,t h e n f(-2)=0 (b) f^(prime)(-1/2)=0 f^(prime)(-1)=-2 (d) f^(0)=4

Consider the function f:(-oo,\ oo)->(-oo,oo) defined by f(x)=(x^2-a x+1)/(x^2+a x+1),\ 0