Simple Calc Derivation

[sysD]

Hi, I want to find the derivative of this but I can't use the quotient rule. So I figure I'll use the chain/product rule.

 

 

I'm new to calc though.Do I use both? Or just one?

 

This is the chain rule I think. Do I go on to use the product rule?

Edited January 19, 2012 by sysD

[Cap'n Refsmmat]

[math]3x(x^2+4)^{-1}[/math]

 

You're going backwards, I think. This is the product of two functions, [math]3x[/math] and [math](x^2+4)^{-1}[/math]. You need to find the derivative of each so you can use the product rule. Taking the derivative of the second will require using the chain rule, of course.

 

Do each piece separately and then put them together to find the derivative of the whole function. I think that's easiest.

[Fuzzwood]

What's wrong with the quotient rule? Just factor out 3 and use x/(x²+4)

[sysD]

[math]3x(x^2+4)^{-1}[/math]

 

You're going backwards, I think. This is the product of two functions, [math]3x[/math] and [math](x^2+4)^{-1}[/math]. You need to find the derivative of each so you can use the product rule. Taking the derivative of the second will require using the chain rule, of course.

 

Do each piece separately and then put them together to find the derivative of the whole function. I think that's easiest.

 

 

[math]f(x)=3x(x^2+4)^-1[/math]

.

[math]f'(x)=3(x^2+4)^power-1 + (3x)(-1)(2x)(x^2+4)^power-2[/math]

 

[math]f'(x)=(3(x^2+4)^2-6x^2(x^2+4))/((x^2+4)(x^2+4)^2[/math]

 

Sorry, the math script doesn't seem to be working for negative exponents.

 

 

Reduce:

 

[math]3(x^2+4)^2-6x^2)/(x^2+4)^2[/math]

 

Is that correct?

 

 

note: (further simplification & factoring)

 

[math](3(x^2+4-2x^2)) / ((x^2+4)^2[/math]

.

[math]3(4-x^2)/(x^2+4)^2[/math]

Edited January 20, 2012 by sysD

[Cap'n Refsmmat]

For negative exponents, you need to put the exponent in curly braces, as in x^{-4} -- otherwise LaTeX just thinks only the first letter is part of the exponent, and just superscripts the - sign.

 

The first part of your work looks good, but when you get to the third line I'm not sure what's happening -- there's more opening parentheses than closed parentheses, so I don't know what goes with what. You took the derivative correctly, though.

[sysD]

Thanks capnI was hoping to get two more answers checked and didn't want to start another topic...

 

1)

Find the points on the curve [math]y=2/(3x-2)[/math] where tangent is parallel to the line [math]y=-(3/2)x-1[/math]

 

my answer coordinates:

(0,-1), (4/3, 1)

 

 

2)

find the equation of the tangent to [math]y=x^2-3x-4[/math] that's parallel to [math]y=7x+3[/math]

 

My answer:

 

y = 7x - 29

[the tree]

Yeah both of those answers are correct.

[sysD]

thanks, thetree