derivatives: slopes and tangents

ok im back lol
ok i dont understand the derivative u got for #43... when i did it i got -8x^2/(x^2+1)^2
 
Please reply showing your steps and your reasoning. Please include a clear statement of what "#43" is and what its instructions are. Thank you.

Eliz.
 
43) find the tangents at the origin and the point (1,2) of y=4x/(x^2+1)

45) the curve y=ax^2+bx+c passes thru the point (1,2) and is tangent to the line y=x at the origin... find a,b,c
 
And what were your steps when you differentiated? (We cannot help you find your error, if you don't show what you did.)

Eliz.
 
ok when u take the derivative.. u go 4x(x^2+1)^-1
then u take the derivative -4x(x^2+1)^-2 (2x)
so u get -8x^2/(x^2+1)^2?
 
The product rule is as follows:

. . . . .(d/dx)(fg) = f'g + fg'

You appear to have done fg', without any f'g.

Eliz.
 
i thot u were supposed to do the power rule then the chain rule.. not the product rule
 
Since you have a product, 4x multiplied by (x<sup>2</sup> + 1)<sup>-1</sup>, the product rule would apply. Within the product rule, though, you would apply the chain rule and the power rule.

Eliz.
 
I already know how to get the derivative. You need to learn. Please apply the rule suggested, or, since you started with a quotient, just apply the quotient rule.

Eliz.
 
This is the same result you got before, and it is still not correct.

You have f = 4x.

You have g = (x<sup>2</sup> + 1)<sup>-1</sup>.

You have the formula, (fg)' = f'g + fg'.

Differentiate f.

Differentiate g.

Plug the results into the formula.

Simplify.

Eliz.
 
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