Question

Find the derivative of f(x)= (1+2x²)(x-x²) in two ways: by using the Product Rule and by performing the multiplication first. Do your answers agree?

Answer 1

Explanation:

Let f(x)= x²= 3. But

2x² = (3x²) = (4x²) = (5x²). So

f(x) = 4x².

The derivative of f (x)=x²=(1+x²) is simply f(x)=x²+1, or 2x².

Dividing both sides by x gives

f(x)=4x² + (1+x²).

Now let x=5