Differentiate the following equation

[Blablablabla]

Homework Statement

Differentiate

s = Tan $^{2}$(e$^{4t}$)

Homework Equations

[e$^{u}$]' = u' e$^{u}$

[Tan(θ)]' = Sec$^{2}$(θ)

Sec(θ) = $\frac{1}{Cos(θ)}$

The Attempt at a Solution

s' = 2[Tan(e$^{4t}$)] * Sec$^{2}$(e$^{4t}$) * 4e$^{4t}$

s' = 8e$^{4t}$ * Tan(e$^{4t}$) * Sec$^{2}$(e$^{4t}$)

s' = 8e$^{4t}$ * $\frac{Tan(e^(4t))}{Cos^2(e^(4t))}$



Mathway says that s' = 0... Can someone please let me know where I went wrong? Thanks

 

[BloodyFrozen]

You're derivative is right. Are you sure they didn't ask you to evaluate the derivative at some point? I'm guessing that they want you to evaluate it at 0.

 

[Blablablabla]

Yes, you're right, I have to find s'(0) aka v(0)

I end up getting this:

v(0) = 8e$^{0}$ * $\frac{Tan(e^0)}{Cos^2(e^0)}$

v(0) = 8 * $\frac{Tan(1)}{Cos^2(1)}$

Is that good?

 

[BloodyFrozen]

Yes, you're right, I have to find s'(0) aka v(0)

I end up getting this:

v(0) = 8e$^{0}$ * $\frac{Tan(e^0)}{Cos^2(e^0)}$

v(0) = 8 * $\frac{Tan(1)}{Cos^2(1)}$

Is that good?

Yes, it is.