Find f'(x): Product Rule for Derivative of (3x^4)(6/(3√x^5)) (6x^2 - 3x)^5

[Stanc]

Homework Statement

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

The Attempt at a Solution

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

 

[Jorriss]

Think makes no sense to me.

What are you trying to do?

 

[haruspex]

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

 

[Stanc]

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

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"

 

[Jorriss]

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"

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?

 

[Stanc]

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?

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 don't know what more I can tell you...

 

[haruspex]

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 don't know what more I can tell you...

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

 

[Stanc]

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

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

 

[haruspex]

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

Sorry, I was confusing two questions. Your answer looks right.

 

[Stanc]

Sorry, I was confusing two questions. Your answer looks right.

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

 

[haruspex]

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

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

 

[Stanc]

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

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?

 

[haruspex]

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?

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