# Trig Differentiation

1. Nov 27, 2011

### jsmith613

1. The problem statement, all variables and given/known data

how is the differential of 1+tan2(4x)

8*tan(4x)*sec2(4x)

2. Relevant equations

3. The attempt at a solution
So 1 differentiates to 0 (we can now ignore this)
tan2(4x) differentiates to 2*tan(4x)*sec2(4x)?

BRING POWER FORWARD, DOWN POWER BY 1, DIFFERENTIATE TERM IN BRACKET
by the chain rule?

2. Nov 27, 2011

### BloodyFrozen

You stated it in your question, but never differentiated the term inside inside the bracket.

$$2 \cdot tan(4x)sec^{2}(4x) \cdot \frac{d}{dx} (4x)~=~$$

Last edited: Nov 27, 2011
3. Nov 27, 2011

### jsmith613

hold on
yours goes to 32....
NOT 8...

4. Nov 27, 2011

### BloodyFrozen

My mistake :tongue: I fixed it in my first post ( coefficient was originally wrong), but my point still holds. You ALSO need to differentiate the 4x.

5. Nov 27, 2011

### jsmith613

oh of course
differentiate u2 = 2u
differentiate sec2(4x) is 4*sec(4x)*tan(4x)
multiply differntials to give
2*sec(4x)*4*sec(4x)*tan(4x)

6. Nov 27, 2011

Exactly!!