# Math Help - equation of the tangent line to the curve

1. ## equation of the tangent line to the curve

determine the equation of the tangent line to the curve
f(x)=4x^3(x-2)^4(6x-5)^5 at point (1,4)

can u just help to get F'(x) then i know how to plug 1 in f'(X).

2. Originally Posted by Max10
determine the equation of the tangent line to the curve
f(x)=4x^3(x-2)^4(6x-5)^5 at point (1,4)

can u just help to get F'(x) then i know how to plug 1 in f'(X).

use the product rule (with the chain rule where necessary) and note that:

if $f, g, \text{ and } h$ are functions of $x$, then

$\frac d{dx} [fgh] = f'gh + fg'h + fgh'$

here you can let $f = 4x^3$, $g = (x - 2)^4$, and $h = (6x - 5)^5$

and note that you need the chain rule to find $g'$ and $h'$

3. so is it f'(x) 12x^2 g'(x)=4(x-2)^3(x) h'(x)=5(6x-5)^4(6)

4. Originally Posted by Max10
so is it f'(x) 12x^2 g'(x)=4(x-2)^3(x) h'(x)=5(6x-5)^4(6)

5. Originally Posted by Jhevon

how come (x-2)^4

g'(x) 4(x-2)^3(x)