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.