# Help Needed With Differentiation!

#### rozzer123

##### New member
Hello,

I've been going through my textbook and I am currently working through the Differentiation topic. I feel like I'm getting a good grip with the concepts (such as the chain rule, etc.), but I've been stuck on this problem for quite some time.

Here is the question:

Here is my working thus far:

Let $$\displaystyle u = 1+bx$$, then $$\displaystyle u' = b$$.

Hence, $$\displaystyle y = au^{-1/2}$$ and $$\displaystyle y' =$$$$\displaystyle \dfrac{-a}{2}$$$$\displaystyle u^{-3/2}$$.

Therefore, $$\displaystyle \dfrac{dy}{dx} = \dfrac{dy}{du} * \dfrac{du}{dx} = \dfrac{-a}{2}u^{-3/2} * b$$.

Substitute u in $$\displaystyle \dfrac{dy}{dx}$$;

$$\displaystyle \dfrac{dy}{dx} =$$$$\displaystyle \dfrac{-a}{2}$$$$\displaystyle (1+bx)^{-3/2} * b$$.

Since $$\displaystyle \dfrac{dy}{dx}$$ = $$\displaystyle \dfrac{-3}{8}$$ at point (1,1)

$$\displaystyle \dfrac{-3}{8}$$ = $$\displaystyle \dfrac{-a}{2}(1+bx)^{-3/2} * b$$.

Therefore, substituting x as 1: $$\displaystyle \dfrac{-3}{8}$$ = $$\displaystyle \dfrac{-a}{2}(1+b)^{-3/2} * b$$.

So, $$\displaystyle \dfrac{-3}{8}$$ = $$\displaystyle \dfrac{-ab}{2(1+b)^{-3/2}}$$.

(I know the index rules regarding the {-3/2}, I just couldn't find a way to type in the root symbol in the coding program :3... even from there, I have no idea where to go!)

Am I approaching the problem correctly? I feel like, after this step, I've been spiraling around - never able to arrive at the correct solution. I've attempted solving for the polynomial roots, using simultaneous equations.. but all have stopped at a dead end.

Could someone help me out? Any advice will genuinely be appreciated

Last edited:

#### Jomo

##### Elite Member
Your last equation is not correct.

After that you should get 2 equations both involving a and b. Solve that system to find a and b

#### Harry_the_cat

##### Senior Member
Obtain the secong equation by substituting x=1 and y=1 into the original eqtn.

#### Jomo

##### Elite Member
Obtain the secong equation by substituting x=1 and y=1 into the original eqtn.
You're so nice.

#### rozzer123

##### New member
Your last equation is not correct.

After that you should get 2 equations both involving a and b. Solve that system to find a and b
Alright. Thank you so much!

#### rozzer123

##### New member
S
Obtain the secong equation by substituting x=1 and y=1 into the original eqtn.
Thank you. I didn't think about looking back at the original equation to obtain the second equation!

#### Jomo

##### Elite Member
So what results did you get for a and b. Please post back. It will help other students with similar problems.