Question

Find the derivative and do not simplify. I will thumbs up if anyone can help

(1-4x)3 d) y = In (3x+2)5 e) y = ( 5x – sin3x)8 f) y = log. (x csc x) g) y = x 5x

Answer 1

3 d) y = ln ( (1-4X) (3x + 2)5 3 ln (1-4) 5 ln (3x+2) on differentiating with sespeet tox. 3 dln (1-4x) . d (1-4) 5d In Bup2) 2(3x+2) d(1-4x) de x+2) dx dy Jx 3. (0-4) -5.1 (3+0) (3x+2) (1-4X) こ - 12 Hence, dy da 1-4X 30+ 2 with respect to a. on e) y = (5x- sinxj8 differentiating dy dx d (5x-sin) こ d (5x-sin3x) 8 d(5x-sin3x) da 5 da a sinx dn d (sinx. d sinu = 8 (50-55m3x 8-1 dx - Hence, dy dx f logero on = 8 (54- Sin3x)? (5613 - 3 sin²x. 68x) 8 (5-3 sin?@). Cox W) (sX-sin'x)? y = log (x CBC x) = log/xesx) = logem + loge ESCX) loge differentiating with respect tox. ( dloge ) d logelesex). d (CSCX) d (esx) dx [ 1 (-esca Cota) ) ) logo (CSOK dy Ja [ - Cotex) dy + da dx L + x Hence,

g) y = 5x on differentiating telith respecto. y = x5x on 9) taking In both sides we get In cys 2 (5x). Inco differentiating with respect to x, d Enly) dy slnas dx ах du dy + sln() () y In sud lncus + dx dy اد) dy こ an (5+5 ln (2) y syllt ln(a) = So, dy In Hence, dy In 5 (xSX) (i+19(x) Note: O - 2 nxn, Corsa d sina dx dan an dlnom ③ a I x 4 = 1 da dloge (X) dr In ming - in m flume 5 In mon) = nlnm) 6 7 log (²) = loge x log = legm-logn