How do you differentiate #f(x)=(x^3-3x)(2x^2+3x+5)# using the product rule?
The answer is
According to the product rule,
This just means that when you differentiate a product, you do derivative of the first, leave second alone, plus derivative of the second, leave the first alone.
So the first would be
Okay, now the derivative of the first is
The derivative of the second is
Multiply it by the first and get
Add both portions together now:
If you multiply it all out and simplify, you should get
The product rule states that for a function,
By applying the power rule, we see that;