In 3 4 8 15 22 25 30 37 and 38 differentiate the given funct

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).

Solution

3.f(x)=xe^x

f\'(x) =x (de^x/dx)+ e^x(d x /dx) =xe^x+e^x

4. f(x)= e^x/x

f\'(x)= x(d e^x/dx)-e^x(dx/dx)/(e^x)²

= (xe^x-e^x)/x²