Question

Calculate the following derivative. (Assume a and b are constants.)
d/dx ((ax + b)(abx^7 + 3))

Answer 1

`(d)/(dx) (ax+b)(abx^7+3) =`

Apply the product rule:
`(f *g) ^(') = f^(') *g+f*g {'}`


`f=ax+b , g=abx^7+3`


`(d)/(dx) (ax+b)(abx^7+3)+ (d)/(dx) (abx^7+3)(ax+b)`


`(d)/(dx) (ax+b)=a`


`(d)/(dx) (b)=0`


`a+0 = a`


`(d)/(dx) (abx^7+3) :`


`(d)/(dx) (3)=0 ; 7 abx^6+0`

Simplify:


`a(abx^7+3)+7abx^6(ax+b)`


`= 8a^2bx^7+3a+7ab^2x^6`

hope this helps!