calculate derivative of the following a lnx ln2x b x2ln x c

calculate derivative of the following:

(a). ln(x) ln(2x)

(b). x^2ln (x)

(c). x^2 2x

Solution

(a) ln(x) ln(2x)

   d[ln(x) ln(2x)] /dx = d[ln(x)] * ln(2x) + ln(x) * d[ln(2x)]/dx

                           = 1/x * ln(2x) + 1/x*ln(x)

                           = [ln(2x) + ln(x)] / x

(b) x²ln(x)

   d(x²ln(x) / dx = d(x²)/ dx * ln x + x² d(lnx)/dx

                       = 2x * lnx + x² * 1/x

                       = 2xlnx + x

(c) x²2x

   d(x²2x)/dx = 6x²