Question

dy For the following composite function, find an inner function u = g(x) and an outer function y=f(u) such that y=f(g(x)). Then calculate dx y=tan (2x)

Answer 1

Solution O given Yo tom (225) let : 2x5 키 outer function ya fp90x)] U = 2 x y = f(u) such that du = 2x5xt sxt ar dy da loxt dx ond Y- flu) Z tom u = dy du secu according to chain rule dy z du dy n du ca X dx dy sec²ux lox4 u + dae put u=goy = x5 7 dy da see? (2 x 5) xloxt hence 4 2 dy do a 1000 see (225) 12 7 Y = (5x-19) let uz 5x-19 du = 5 da. => Yzu? = 746 7. dy dx Tu du die dy du Z х dy ㅋ 748x5 Z da put u= 52-19 6 لابل dir 35 ( 52-19 dx

3 golen 4.4 2337 at @ peuforming impleat differentiation 4x3+4 13 dy dx 3 dy dx x a y3 © cet 64,3), 3 dy da (-4) NI 33 dy 64 27 dx dly du Slope is given by hence slope of 27 yt = 337 at (-4,3) is 64 27