Trig Differentiation for tan2(4x): Solving 1+tan2(4x) using the Chain Rule

[jsmith613]

Homework Statement

how is the differential of 1+tan²(4x)

8*tan(4x)*sec²(4x)

Homework Equations

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?

 

[BloodyFrozen]

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

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)~=~

 

[jsmith613]

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

 

[BloodyFrozen]

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

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

 

[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)

 

[BloodyFrozen]

Exactly!