Question

How do you differentiate `f(x) =cos(3x -2)-tan(4x+3)`?

Answer 1

`-3sin(3x-2) -4sec^2(4x+3)`

Explanation:

differentiate using the`color(blue) " chain rule "`

`d/dx[f(g(x))] = f'(g(x)).g'(x)`

and the standard derivatives :

`d/dx(cosx) = -sinx " and " d/dx(tanx) = sec^2x`

`f'(x) = -sin(3x-2) d/dx(3x-2) - sec^2(4x+3) d/dx(4x+3)`

`= -sin( 3x-2).3 - sec^2(4x+3).4`