Differentiate the function f(x)= 2x^2 - 5x - 3?

Question

a. Differentiate the function f(x)= 2x^2 - 5x - 3
b. Factor the function in part a and differentiate by using the product rule. Show that the two answers are the same.

Simplify answers and please show work
I'M REALLY TRYING TO GRASP THIS CONCEPT

Answer 1

f(x) = 2x^2-5x-3
f'(x)=4x-5

f(x) = 2x^2-5x-3
f(x) = (2x+1)(x-3)
f'(x)=(2x+1)(1) + (x-3)(2)
f'(x)= 2x+1+2x-6
f'(x)=4x-5

Answer 2

This is a VERY simple derivative. If you are having trouble with this, that means that you are not grasp[ing the most basic facts.

In order to do this, you need to use four rules. They are:

1. The derivative of a constant is zero.

2. The derivative of a sum of things is the sum of the derivatives. That is: d(Y+Z)/dx = dY/dx+dZ/dx

3. The derivative of a constant times a function is equal to the constant times the derivative of the function. That is: d(c*Y)/dx = c*dY/dx

4. The power rule. It says that d(x^n)/dx = n*x^(n-1).

Using these rules, the derivative of the above function is:

2*(2x) - 5 = 4x-5

To do part b, you need to factor the binomial to get:

2x^2-5x-3 = (2x+1)(x-3)

You can then differentiate that using the product rule. That is:

d(Y*Z)/dx = Y*dZ/dx +Z*dY/dx = (2x+1)*(1) + (x-3)*(2)