Question

find f'(x) and simplify

f(x) = x^2+1/2x-3

Answer 1

hi can you please explain to me in a simple easy fast way and with steps also

Answer 2

https://answers.yahoo.com/question/index?qid=20100120231452AAkwR82

Answer 3

That should help!

Answer 4

yes but I need someone to help me solve this visually

Answer 5

Sorry I don't know but @mathmale should.

Answer 6

@thomaster @tester97 @mathmale @Lena772 @DollyAcquah @Destinymasha @bashirk

Answer 7

Use the power rule for the first one. Then on the second apply quotient rule.

Answer 8

can you do it for me so I can see how you do it and then I will learn

Answer 9

as this is is my first time learning this and I am more of a visual learner

Answer 10

Power rule: Bring down the power and subtract one from it.
Quotient rule: \(\LARGE (\frac{f(x)}{g(x)})'=\frac{g(x)f'(x)-g'(x)f(x)}{(g(x))^2}\)

Answer 11

Basically here, you have to differentiate each term with respect to x. Yes, that's it!
Here is how it goes.
I think this is what you mean by the question:

\[f(x) = \frac{x^2 + 1}{2x-3}\]
\[f'(x) = \frac{d (\frac{x^2 + 1}{2x-3})}{dx}\]

Now as @Luigi0210 said, you have to use the quotient rule to find out the derivative of an expression where you have the denominator and the numerator as polynomials.

After using that you'd get something which looks like this:
\[f'(x) = \frac{(2x-3)\frac{d(x^2+1)}{dx} - (x^2+1)\frac{d(2x-3)}{dx}}{(2x-3)^2}\]

Now you just have to find the derivative wrt x.

Getting this? :D

Answer 12

is there a much easier and simpleer shortcut to get the anser rathen that all of this

Answer 13

lke can I go this on a ti83 graphing calculator

Answer 14

No, none I am aware of.
You may try using logarithms to get rid of the quotient rule by directly using chain rule but apart from that, I don't think so. Plus, this shouldn't be much work. I say, give it a shot once, it is not too long.
Just differentiate the terms using chain rule and the multiplication then shouldn't be hard.
I am not very sure about the ti83 calculator, my calculator 'casio 9860gii' calculates derivatives when the value of x is given. I suggest you ought try and find a video on that on youtube. :D

Answer 15

Differentiation is done by hand.. calculus is mainly algebra, not plugging in numbers into a calculator(not till the end at least). Can't always rely on calculators.

Answer 16

I have another question find f ' (x) and find the equation of the line tangent to the graph of f at x=2

f(x) = (1+3x)(5-2x)

Answer 17

just please help me with these two questions and pleae explain how to do them and if they have a shortcut to these promblems please tell me and leave it on this site

Answer 18

Yes, @Luigi0210 is absolutely right!

Well, for you next question @toxicsugar22 you need to use the product rule to solve.

Product rule: \(d.f * d.g = g*d.f + f*d.g\)

An alternative would be, multiply the to binomials, then find their derivative using the chain rule.

f'(x) would then give you the slope of the line tangent to f(x) for any real value of x.
Thus, you can find f'(2) which gives the tangent of the function at x=2.
That would be your slope, you can see to what I am hinting at. You might have guessed it, now you need to use the point slope form of a line! Not so fast though.

Calculate y = f(2) [Which gives the y value of the curve at x=2]

Use (x,y) and f'(2) to find the equation of tangent to the curve f(x) at x=2.

Understood? :)

Answer 19

I'd be honest with you, there are many methods to do this. The only shortcut to math is to practice it.

Answer 20

@toxicsugar22: The Product Rule, the Quotient Rule and the Chain Rule are basic formulas for derivatives that you'll see again and again. I strongly suggest that you learn all three by practicing them.

Product rule: d.f∗d.g=g∗d.f+f∗d.g (provided by AskashdeepDeb) appears mathematically correct, but in the USA a more common way of writing the Product Rule is\[\frac{ d }{ dx}u*v=u*\frac{ dv }{ dx }+v*\frac{ du }{ dx }\] where u*v signifies the product of the functions u and v.

Answer 21

You want to find the derivative of f(x) = (1+3x)(5-2x), a product? Start by identifying:
u, v, du/dx and dv/dx.

Can you put together the resulting four algebraic expressions to form the derivative of the given f(x), where f(x) = (1+3x)(5-2x)?

Answer 22

quotient rule > product rule