Plot[
      ArcSin[x], {x, -1, 1}]

NIntegrate[ArcSin[x], {x, -1, 1}]

Plot[{Exp[x], 2 + Log[x + 1]}, {x, - .5, 2}]

FindRoot[Exp[x] == 2 + Log[x + 1], {x, 1}]

The two functions intersect at the x - 
      coordinate .989.

NIntegrate[2 + Log[x + 1] - Exp[x], {x, - .5,  .989}]

NIntegrate[Exp[x] - 2 + Log[x + 1], {x,  .989, 2}]

1.12126 + 3.59565

The area bounded by the two functions is 4.71691.

Plot[ArcSin[3  x], {x, -1, 1}]

-10/-2

(1/
          5) is the slope of the line passing through (2, -3) and (4, 7)

D[ArcSin[3  x], x]

G[x] = D[ArcSin[3  x], x]

Solve[G[x] == 5, x]

ArcSin[3 (4/15)]

N[%]

ArcSin[3 (-4/15)]

N[%]

The graph of ArcSin[
        3  x] has a slop of 5 at (2.67,  .927) and (-2.67, - .927)