Derivatives of Trig Functions

Derivatives of Trig Functions

I’m sure you’ve seen these before, but here are the derivatives of the basic trig functions:

    d/dx(sin u) = cos u du/dx

    d/dx(cos u) = -sin u du/dx

    d/dx(tan u) = sec2 u du/dx

    d/dx(cot u) = -csc2u du/dx

    d/dx(sec u) = sec u tan u du/dx

    d/dx(csc u) = – csc u cot u du/dx

You should probably memorize the first three of these.

Now, let’s take the derivative of this function:

        y = sin(2x2 +4)

        Let u (2x2 +4)         then du/dx = 4x.

       So    dy/dx = cos(2x2 +4) 4x

Try this one:     y = cos(5x3 + 6x)

    Take dy/dx and click here when you’re done.

        dy/dx = -sin(5x3 + 6x) (15x2 + 6)