FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.31Example 64 : y = log (4x), find dydx
Solution:Let y = log u, where u = 4x, ddxu=^4
dx du dx dudy dy du d= = (log u. 4) =u^1 ⋅4 4.= 4x x1 1=.Example 65 : y = log (1 x ,+ ) find dydx
Solution:Let y = log u, where u = 1 x+
( )
du 0 1 1 dy dy du 1 1;.. 1
dx= +2 x 2 x= dx du dx u= = 2 x= 1 x. 2 x+Example 66: Find dydx if y = (2x – 5)^6.
Solution:Let y = z^6 , where z = 2x – 5, dxdz=^2
dx dz dx dzdy dy dz d=. = (z .2 6z .2 12z 12 (2x 5)^6 ) =^5 =^5 = −^5Example 67: If y x 7,=^2 + find dydx.
Solution: Let y = z, where z x 7,=^2 + dxdz=2x.
dy dy dz d.. z.
dx dz dx dz= = 2x^2(^1). 2x x x
2 z z x 7
= = =
+
Example 68: If y =(x 2x 5x ,^3 +^2 + )−^3 find dydx
Solution: Let y = u – 3, where u = x^3 + 2x^2 + 5x,
du 3x 4x 5 2
dx= + +dy 3u 4
du= − −
(^3) ( (^2) )
dy dy du d.. u. 3x 4x 5
dx du dx du
= = − + +
= – 3.u– 4. (3x^2 + 4x + 5) = – 3 (3x^2 + 4x + 5). (x^3 + 2x^2 + 5x)– 4