Answer:
see explanation
Step-by-step explanation:
Using the chain rule
Given
y = f(g(x)), then
= f'(g(x)) × g'(x) ← chain rule
and the standard derivatives
(
x ) = 
, (lnx) = 
(a)
Given
y = 
= 
× (
= × 
× (1 + x)
= × 
× 1
= 
= 
(b)
Given
y = ln sinx
= 
× (sinx)
= × cosx
= 
= cotx
so first off, let's simplify both equations, starting off by multiplying both sides by the LCD of all fractions, to do away with the denominators.
![\bf \cfrac{10(x-y)-4(1-x)}{3}=y\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{10(x-y)-4(1-x)=3y} \\\\\\ 10x-10y-4+4x=3y\implies \boxed{14x-13y=4} \\\\[-0.35em] ~\dotfill\\\\ 7+x-\cfrac{x-3y}{4}=2x-\cfrac{y+5}{3}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{12}}{12\left( 7+x-\cfrac{x-3y}{4} \right)=12\left( 2x-\cfrac{y+5}{3} \right)} \\\\\\ 84+12x-3(x-3y)=24x-4(y+5) \\\\\\ 84+12x-3x+9y=24x-4y-20\implies \boxed{-15x+13y=-124}](https://tex.z-dn.net/?f=%5Cbf%20%5Ccfrac%7B10%28x-y%29-4%281-x%29%7D%7B3%7D%3Dy%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Bmultiplying%20both%20sides%20by%20%7D%5Cstackrel%7BLCD%7D%7B3%7D%7D%7B10%28x-y%29-4%281-x%29%3D3y%7D%20%5C%5C%5C%5C%5C%5C%2010x-10y-4%2B4x%3D3y%5Cimplies%20%5Cboxed%7B14x-13y%3D4%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%207%2Bx-%5Ccfrac%7Bx-3y%7D%7B4%7D%3D2x-%5Ccfrac%7By%2B5%7D%7B3%7D%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Bmultiplying%20both%20sides%20by%20%7D%5Cstackrel%7BLCD%7D%7B12%7D%7D%7B12%5Cleft%28%207%2Bx-%5Ccfrac%7Bx-3y%7D%7B4%7D%20%5Cright%29%3D12%5Cleft%28%202x-%5Ccfrac%7By%2B5%7D%7B3%7D%20%5Cright%29%7D%20%5C%5C%5C%5C%5C%5C%2084%2B12x-3%28x-3y%29%3D24x-4%28y%2B5%29%20%5C%5C%5C%5C%5C%5C%2084%2B12x-3x%2B9y%3D24x-4y-20%5Cimplies%20%5Cboxed%7B-15x%2B13y%3D-124%7D)
now, let's do some elimination on those two simplified equations.
![\bf \begin{array}{cllcl} 14x&-13y&=&4\\ -15x&+13y&=&-124\\\cline{1-4} -x&&=&-120 \end{array}~\hfill x=\cfrac{-120}{-1}\implies \blacktriangleright x=120 \blacktriangleleft \\\\\\ \stackrel{\textit{substituting on the 1st equation}}{14(120)-13y=4}\implies 1680-13y=4\implies 1680-4=13y \\\\\\ 1676=13y\implies \blacktriangleright \cfrac{1676}{13}=y \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \left( 120~,~\frac{1676}{13} \right)~\hfill](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Barray%7D%7Bcllcl%7D%2014x%26-13y%26%3D%264%5C%5C%20-15x%26%2B13y%26%3D%26-124%5C%5C%5Ccline%7B1-4%7D%20-x%26%26%3D%26-120%20%5Cend%7Barray%7D~%5Chfill%20x%3D%5Ccfrac%7B-120%7D%7B-1%7D%5Cimplies%20%5Cblacktriangleright%20x%3D120%20%5Cblacktriangleleft%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Bsubstituting%20on%20the%201st%20equation%7D%7D%7B14%28120%29-13y%3D4%7D%5Cimplies%201680-13y%3D4%5Cimplies%201680-4%3D13y%20%5C%5C%5C%5C%5C%5C%201676%3D13y%5Cimplies%20%5Cblacktriangleright%20%5Ccfrac%7B1676%7D%7B13%7D%3Dy%20%5Cblacktriangleleft%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20~%5Chfill%20%5Cleft%28%20120~%2C~%5Cfrac%7B1676%7D%7B13%7D%20%5Cright%29~%5Chfill)
Answer: Remeber 2+2=5 and
Step-by-step explanation: if yur on fire stop drop and roll do it and your awesome. Another thing is if someones taking forever drinking water when your behind them sing 123 can you hurry up please 456 imma hit you with a brick 789 imma spit this sick ryme
Answer: X=-24
Step-by-step explanation:
You would have to divide 5 by 12 then multiply by 30 which gives you $12.50
