1. ## some mixed problems...

Hello, if anybody could help me with these problems I would greatlly appreciated it! If you could give me details to the solutions I would really appreciate it as well...

get the first, and second derivaties and graph the functions:
1) sin(e)^x

2) (2(e)^2x - 7e)/(5(e)^3x - 7(e)^2x + 5)

3) sec(ln(x))

4) (1/2)ln((1 + x)/(1 - x))

thank you again...

2. Originally Posted by onmiverse
get the first, and second derivaties and graph the functions:
1) sin(e)^x
You want the first two derivatives of:

$f(x)=\sin(e^x)$

You will need the chain rule for the first derivative:

$\frac{d}{dx}h(g(x))=h'(g(x))g'(x)$

Here $g(x)=e^x$ and $h(x)=\sin(x)$

For the second you will need the cain rule again but also the product rule.

CB

3. What was written for (1) was sin(e)^x which I would interpret as $sin^x(e)$, a constant to the x power. That can be written as $e^{sin^x(e)}= e^{xsin(e)}$ and its derivative is $sin(e)e^{xsin(e)}= sin(e)[sin^x(e)]= sin^{x+1}(e)$.

4. Originally Posted by HallsofIvy
What was written for (1) was sin(e)^x which I would interpret as $sin^x(e)$, a constant to the x power. That can be written as $e^{sin^x(e)}= e^{xsin(e)}$ and its derivative is $sin(e)e^{xsin(e)}= sin(e)[sin^x(e)]= sin^{x+1}(e)$.
It is more likely just sloppy typing by the OP for $\sin(e^x)$ given the other questions. No doubt they will tell us eventually.

CB