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) = sec^{2 }u du/dx

d/dx(cot u) = -csc^{2}u 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(2x^{2} +4)

Let u (2x^{2} +4) then du/dx = 4x.

So dy/dx = cos(2x^{2} +4) 4x

Try this one: y = cos(5x^{3} + 6x)

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

dy/dx = -sin(5x^{3} + 6x) (15x^{2} + 6)