# Find the Derivative

1. Mar 20, 2013

### Stanc

1. The problem statement, all variables and given/known data

Find dy/dx: 4a^2b - 3b^2 = a^3 Please SIMPLIFY this one

Find f'(x): f(x) = (3x^4) [6/(3√x^5)] (6x^2 - 3x)^5 The middle is 6 divided by the cube root of x^5, Please do not simplify fully for this one and use the product rule

3. The attempt at a solution

i got - (8ab - 3a^2)/(4a^2 - 6b) using the implicit rule
However I need some help simplifying

For the second one, would my approach be (derivative of first)(original second)(original third) + (derivative of second)(original first)(original third) + (derivative of third)(original first)(original second) ?

Last edited: Mar 20, 2013
2. Mar 20, 2013

### Jorriss

Think makes no sense to me.

What are you trying to do?

3. Mar 20, 2013

### haruspex

Your approach for the second is fine. The first is unintelligible. Please check what you wrote.

4. Mar 20, 2013

### Stanc

Is this not the result of the implicit method? Should I not even be using the implicit method? I thought I had to with numerator being the derivative with respect to "a" and the denominator the derivative with respect to "b"

5. Mar 20, 2013

### Jorriss

How should we know what you need to do if its not even clear what you're question asking?

You just simply said Find dy/dx, then gave an expression in terms of a and b then said simplify.

What does that even mean?

6. Mar 20, 2013

### Stanc

Sorry about the a and b, it should be a=x and b = y (teacher gave it to us like that) but the question is to simply find the derivative (dy/dx).... i dont know what more I can tell you...

7. Mar 20, 2013

### haruspex

Ok, but it still doesn't make sense: Find dy/dx: 4x2y - 3y2 = x3. What's the equals sign doing?

8. Mar 20, 2013

### Stanc

I have to set it equal to zero and use implicit differentiation

9. Mar 20, 2013

### haruspex

10. Mar 20, 2013

### Stanc

Ok Thank you! but is that all it can be simplified down to?

11. Mar 20, 2013

### haruspex

You could factorise out an x in the numerator, but other than that, that's as simple as it will go.

12. Mar 20, 2013

### Stanc

May I ask you one more question? How would i find the derivative of (1/x) + (1//y) = 1 using implicit and for a question like (x^2/19) - (y^2/9) = 1 would I find the common denominator and then go through with implicit differentiation?

13. Mar 21, 2013

### haruspex

You can just differentiate straight away. What's the difficulty? Yes, multiplying out first might make it a little simpler.