Question

4. g(t)= 3. y=sin(tan5x)

Answer 1

11s f(x) = sime e-Cosz) (sima) 2 (1-Case) casu I-Cola different rating with respect to t FICU) sime & -cos) (1-Cohe) 2 Sime sinn (1-Come) 2 Coss-Costa asinan (1-Colo) 2 Colul (1-Coh) -1 I-Colu f'n 2 - 그 Cosul to llo a 3770-2) an 3 . giren fn) = [x3 +72-2] disferentiating both sides with respect to a and using chain rille, $161) = 100 [131774–27" [flow = 100 (2774-2) (3x²+7) given that y= sin(tan 54) differentiating both sides with respect to see and using chain rule dys = y'= 3 simptom suy rusting chain rule] = 3 sin (tan 5n) Costansu) atasi = 3 sinesten sn) carstanbu) 5 seen 15 sihatan 54) Coltan 5) seesu) d (sin tansu)) dy che

g. (t) =/2t-1th 4. given that ++3 differentiating both sides with respect to t) [using Chain gl(t)= 4 (2t - 1)3 g/t) + (24-193 ( att t+3 ruke] 기 4 @t-1 45'3 [147326047 (++3) 2 -(2t-D (413) 2 3 =4 27-1 Zt3 276-2+1 (ZF 3) 2 = 28 Qt-1)3 2) gle (t +35 5 . $20 sex) = Cos (² esen diferenttating both sides with respect to 're and using chain rule f'(n)= -sin (M3 esex) Wesen) -sinfiles.cz) [siese x cotxe +sa+eser] » [ f'M) = -sin Gesex) esen [3ve? Best ] du =

lim N73 sin (1-3) 30-x2 since we have an indeterminate form of type of we can apply the Ľ Hopitals rule lim da Sin Q1-3)) u-x2) 173 1) lim lx cos((-3) +3 3-2x - lim +3 sin (1-3) 31-22 - -ใๆ 1 3 3