find the derivative f(x) = (x + 3) (x + 1)?

Question

I need problem worked out please. Thanks everybody.

Answer 1

f(x) = (x + 3)(x + 1)
f(x) = x^2 + x + 3x + 3
f(x) = x^2 + 4x + 3

f'(x) = 2x + 4

-----------------------------------------

Another way to do this

f(x) = (x + 3)(x + 1)

f'(x) = (x + 3)'(x + 1) + (x + 3)(x + 1)'
f'(x) = 1(x + 1) + 1(x + 3)
f'(x) = x + 1 + x + 3
f'(x) = 2x + 4

Answer 2

Two ways to do this

Method 1: product rule:

f'(x) = d(x+3)/dx * (x+1) + d(x+1)/dx * (x+3) = x+1+x+3 = 2x+4

Method two: multiply and use the power rule:

f(x) = x² + 4x + 3
f'(x) = 2x+4

Answer 3

For something as simple as this, it's probably best to expand the brackets and differentiate in turn.

So f(x) = x^2 + 4x +3; and f'(x) = 2x+4

Answer 4

f(x) = x² + 4x + 1
f `(x) = 2x + 4

Or could use the Product Rule:-
f `(x) = 1.(x + 1) + 1.(x + 3)
f ` (x) = x + 1 + x + 3
f `(x) = 2x + 4 (as above)

Answer 5

x^2 + 4x + 3

Answer 6

(fg)' = fg' + f' g = (x + 3)' (x + 1) + (x + 3) (x + 1)' = (x +1) + (x + 3) = 2x + 4 = 2(x +2)

Answer 7

f(x)=x^2+4x+3, the first derivative:
f'(x)= 2x + 4.

Answer 8

f(x) = x^2 + 4x + 3
f'(x) = 2x + 4

Easy. Or you can use the product rule.

f'(x) = u'v + v'u
f'(x) = (1)(x + 1) + (1)(x+3)

Answer 9

f(x)= x^2+4x+3

f`(x) = 2x + 4

Answer 10

since its factored its even easier to use (fg)' = f'g + fg'

1*(x+1) + (x+3)*1 = 2x+4