1. ## College exam questions

Hello my fellow mathematicians,

I joined the forum today, and I hope to integrate well with this forum. I love science subjects and have made an attempt in doing Biology, Physics, Chemistry and Maths.
I'am in urgent need for help in Mathematics as my college midterm exams are getting nearer (12 days left). I intend on using this thread for posting questions that have significantly hindered my progress:

Here goes:

Differentiating exponentials and logarithms:
Question:
Q1, Given that y = 5/1+e^3x, find the value of dy/dx when x = 0.

Q2,Defferentiate each of the following functions with respect to x.

a, 3lnx^-2
b, ln(x^2+x-2)
c, ln(x(x+1))
d, ln 2x+1/3x-1

Trignometry:
Solve the equation sin2@ = 4sin(@-60), show that 2 . 3cos@ = sin@. Hence find the value of @ such that 0<@<360.

Thank you

Regards
pA

2. Originally Posted by Passive_absorber
...
Here goes:

Differentiating exponentials and logarithms:
Question:
Q1, Given that y = 5/1+e^3x, find the value of dy/dx when x = 0.

...
I assume that you mean:

$f(x)=\dfrac5{1+e^{3x}} = 5\left( 1+e^{3x} \right)^{-1}$ If so, use chain rule to get the derivation:

$f'(x)=5\cdot (-1) \cdot \left( 1+e^{3x} \right)^{-2} \cdot e^{3x} \cdot 3 = - \dfrac{15e^{3x}}{\left( 1+e^{3x} \right)^{2}}$

Thus $f'(0)=- \dfrac{15e^{0}}{\left( 1+e^{0} \right)^{2}}=-\dfrac{15}4$

For the next 4 questions use the property that $\dfrac{d(\ln(x))}{dx}=\dfrac1x$ and the chain rule.

3. Originally Posted by Passive_absorber
Hello my fellow mathematicians,

I joined the forum today, and I hope to integrate well with this forum. I love science subjects and have made an attempt in doing Biology, Physics, Chemistry and Maths.
I'am in urgent need for help in Mathematics as my college midterm exams are getting nearer (12 days left). I intend on using this thread for posting questions that have significantly hindered my progress:
Don't do that, rather post one question per thread. Otherwise the thread will become unweildy and difficult to follow/make sense of.

CB

4. I assume that you mean:
Correct. By the way, how do you write the whole thing like that. MS word does not have mathematical syntax.

If so, use chain rule to get the derivation:

Thus

For the next 4 questions use the property that and the chain rule.
Alright thanks for the help, but I have trouble understanding the chain rule used here. Oh and can this:

be used with the chain rule together? I always thought they were seperately done. Oh and please can someone tell me the solution to the Trignometry problem.

Don't do that, rather post one question per thread. Otherwise the thread will become unweildy and difficult to follow/make sense of.

CB
Sure thing. I'll keep that in mind.

5. Originally Posted by Passive_absorber
Correct. By the way, how do you write the whole thing like that. MS word does not have mathematical syntax.
Have a look here: http://www.mathhelpforum.com/math-he...-tutorial.html

Alright thanks for the help, but I have trouble understanding the chain rule used here. Oh and can this:

be used with the chain rule together? I always thought they were seperately done. .........What do you mean by that?

...
I'm going to demonstrate b):

$f(x)=\ln(x^2+x-2)~\implies~f'(x)= \underbrace{\dfrac1{x^2+x-2}}_{\text{der.\ outer\ fct.}}\cdot \underbrace{(2x+1)}_{\text{der.\ inner\ fct.}} = \dfrac{2x+1}{x^2+x-2}$

der. outer fct. means derivation of the outer function