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!!