- T12 In Order To Differentiate Y U Where U And V Are Both Functions Of C One Can First Take Natural Logarithms Of B 1 (220.13 KiB) Viewed 22 times
T12. In order to differentiate y = u', where u and v are both functions of c, one can first take natural logarithms of both sides (lny = v In u) and then differentiate implicitly. This technique, called logarithmic differentiation, is also useful for complicated products and quotients, because of the laws of logarithms. (a) Use logarithmic differentiation to differentiate: (i) zsina e-1 (ii) (sec x) cotx (iii) (arctan x) (iv) (In 2x) In 32 (v) (x2 + x + 1)(x4 + 1)(x2 + 1) (vi) (x2 + 1)1/2(x4 + 1)1/4(x6 + 1)1/6. (b) Find, but do not learn, formulae for the derivatives of u' and U1U2U3U4 ... Un. (c) Find the equations of the tangent and normal to the curve xy = you at the point (2,4). =