1.

Find the derivative of the following functions (it is to be understand that a,b,c,d,p,q,r and s are fixed non-zero constants and m and n are integers): `(ax+b)^(n)(cx+d)^(m)`

Answer» Let `Y=(ax+b)^(n)(cx+d)^(m)`
`rArr(dy)/(dx)=(d)/(dx)(ax+b)^(n)(cx+d)^(m)`
`rArr =(ax+b)^(n)(d)/(dx)(cx+d)^(m)`
`+(cx+d)^(m)(d)/(dx)(ax+b)^(n)`
`=(ax+b)^(n).m(cx+d)^(m-1).(d)/(dx)(cx+d)`
`+(cx+d)^(m).n(ax+b)^(n-1)(d)/(dx)(ax+b)`
`=m(ax+b)^(n) (cx+d)^(m-1).c`
`+n(cx+d)^(m)(Ax+b)^(n-1)`
`=(ax+b)^(n-1)(cx+d)^(m-1)cm(ax+b)+an(cx+d)`


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