Find the derivative of y = (3x +2)(x^2+5)

Find the derivative of y = (3x +2)(x^2+5)? How do I do this? Please help. Thanks in advance.

Two ways to do this:
1. Easiest way is to use the product rule which states if y(x)=f(x)*g(x) then dy(x)=f(x)*dg(x)+g(x)*df(x)
In words it says the derivative of a product of two terms is the derivative of the first term times the second term, plus the first term times the derivative of the second term
So in this case *** dy=3(x^2+5)+(3x+2)(2x) ***

2. Otherwise you can simply multiply out the two polynomials and then differentiate normally:
y = (3x +2)(x^2+5) = 3x^3+15x+2x^2+10
then *** dy= 9x^2+15+4x ***

Notice if you multiply out the result from the first method it equals the result from the second method

You need to use the product rule

d/dx [ f(x) g(x) ] = d/dx [f(x)] g(x) + f(x) d/dx [g (x)]

d/dx [f(x)] = 3

d/dx [g(x)] = 2x

Use these value and substitute in to the product formula

3(x^2 + 5) + (3x + 2)(2x) =

3x^2 + 15 + 6x^2 + 4x =

9x^2 + 4x + 15

y = (3x +2)(x^2+5)
y= 3x(x^2+5) + 2(x^2+5)
y= 3x^3+15x+2x^2+10
y= 3x^3+2x^2+15x+10

if u want this in hard copy solved with all steps contact at tech.online@yahoo.com