In 3, 4, 8, 15, 22, 25, 30, 37 and 38, differentiate the given function. f(x) =
ID: 3015614 • Letter: I
Question
In 3, 4, 8, 15, 22, 25, 30, 37 and 38, differentiate the given function. f(x) = xe^x, f'(x) = f(x) = e^x/x, f'(x) = f(x) = xe^-x^2, f'(x) = xe^-x^2 (-2x) + e^-x^2 = f(x) = x^2 ln x, f'(x) 2x ln x + x^2 1/x = f(t) = t^2 ln (cubicroot t) = t^2 1/3 ln t, h(t) = e^t + t/ln t, h'(t) = f(x) = e^x + e^-x/e^x - e^-x, f'(x) = (e^x - e^-x)(e^x - e^-x) - (e^x 0 e^-x)(e^x + e^-x)/(e^x - e^-x)^2 f(x) = x log_10 x = x ln x/ln(10) = 1/ln(10) = 1/ln(10) (x ln x), f(x) = log_2 = ln x/ln 2 Squareroot x, f'(x) = Log_2 x = ln/ln(2).Explanation / Answer
3.f(x)=xex
f'(x) =x (dex/dx)+ ex(d x /dx) =xex+ex
4. f(x)= ex/x
f'(x)= x(d ex/dx)-ex(dx/dx)/(ex)2
= (xex-ex)/x2