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C1 Question

Could anybody give me some guidance on how to approach this question please? I don't know where to start:

Given that y=5x−7+2x+3x,x>0y = 5x - 7 + \frac{2 \sqrt x + 3}{x}, x > 0
Find dydx\frac{dy}{dx}, simplifying the coefficient of each term.

Thanks guys!
Reply 1
Avatar for Super199
Super199
20
Original post by thomash131
Could anybody give me some guidance on how to approach this question please? I don't know where to start:

Given that y=5x−7+2x+3x,x>0y = 5x - 7 + \frac{2 \sqrt x + 3}{x}, x > 0
Find dydx\frac{dy}{dx}, simplifying the coefficient of each term.

Thanks guys!

Rewrite the second part in terms of indices and split up the fraction. So 2x=2x?2\sqrt x = 2x^?
Reply 2
Avatar for the bear
the bear
20
what Super said. then use the idea

if y = axn

then dy/dx = anxn-1
Original post by thomash131
Could anybody give me some guidance on how to approach this question please? I don't know where to start:

Given that y=5x−7+2x+3x,x>0y = 5x - 7 + \frac{2 \sqrt x + 3}{x}, x > 0
Find dydx\frac{dy}{dx}, simplifying the coefficient of each term.

Thanks guys!


Don't know where to start?
OK, is that "Don't know what dy/dx is and how to find it"?
or
"I can't simplify the equation but I know how to differentiate"?
Reply 4
Avatar for Moonwalker39
Moonwalker39
OP
Original post by the bear
what Super said. then use the idea

if y = axn

then dy/dx = anxn-1


Original post by m4ths/maths247
Don't know where to start?
OK, is that "Don't know what dy/dx is and how to find it"?
or
"I can't simplify the equation but I know how to differentiate"?

I can't simplify it. I know how to differentiate :biggrin:

Original post by Super199
Rewrite the second part in terms of indices and split up the fraction. So 2x=2x?2\sqrt x = 2x^?

So would it be:
2x1/2x+x−3\frac{2x^{1/2}}{x} + x^{-3}?
Reply 5
Avatar for davros
davros
16
Original post by thomash131
I can't simplify it. I know how to differentiate :biggrin:


So would it be:
2x1/2x+x−3\frac{2x^{1/2}}{x} + x^{-3}?


You can simplify 2x1/2x\frac{2x^{1/2}}{x} still further.

And where did you get x−3x^{-3} from?
Reply 6
Avatar for the bear
the bear
20
Original post by thomash131
I can't simplify it. I know how to differentiate :biggrin:


So would it be:
2x1/2x+3x−1\frac{2x^{1/2}}{x} + 3x^{-1}?


2x1/2x+3x−1\frac{2x^{1/2}}{x} + 3x^{-1}
(edited 10 years ago)
Reply 7
Avatar for Moonwalker39
Moonwalker39
OP
Original post by davros
You can simplify 2x1/2x\frac{2x^{1/2}}{x} still further.

And where did you get x−3x^{-3} from?

Because the whole fraction is:
2x+3x\frac {2\sqrt x + 3}{x}
So I split it into two parts:
2xx+3x\frac {2\sqrt x}{x} + \frac {3}{x}
And then attempted to simplify it into:
2x1/2x+x−3\frac{2x^{1/2}}{x} + x^{-3}


Original post by the bear
^^
Does this mean I'm doing okay? Or have I got it wrong? lol
Reply 8
Avatar for the bear
the bear
20
Original post by thomash131
Because the whole fraction is:
2x+3x\frac {2\sqrt x + 3}{x}
So I split it into two parts:
2xx+3x\frac {2\sqrt x}{x} + \frac {3}{x}
And then attempted to simplify it into:
2x1/2x+x−3\frac{2x^{1/2}}{x} + x^{-3}


Does this mean I'm doing okay? Or have I got it wrong? lol


2x1/2x+3x−1\frac{2x^{1/2}}{x} + 3x^{-1}
Reply 9
Avatar for Moonwalker39
Moonwalker39
OP
Original post by the bear
2x1/2x+3x−1\frac{2x^{1/2}}{x} + 3x^{-1}

And would this then be simplified to:
2x−1/2+3x−12x^{-1/2} + 3x^{-1}?
Reply 10
Avatar for davros
davros
16
Original post by thomash131
Because the whole fraction is:
2x+3x\frac {2\sqrt x + 3}{x}
So I split it into two parts:
2xx+3x\frac {2\sqrt x}{x} + \frac {3}{x}
And then attempted to simplify it into:
2x1/2x+x−3\frac{2x^{1/2}}{x} + x^{-3}


Does this mean I'm doing okay? Or have I got it wrong? lol


Wrong!

What is 2x1/2x\frac{2x^{1/2}}{x} when simplified?

Why do you think that 3x=x−3 \frac {3}{x} = x^{-3}?
Reply 11
Avatar for the bear
the bear
20
Original post by thomash131
And would this then be simplified to:
2x−1/2+3x−12x^{-1/2} + 3x^{-1}?


yes... you are heading in the right direction now :wink:
Reply 12
Avatar for Moonwalker39
Moonwalker39
OP
Original post by davros
Wrong!

What is 2x1/2x\frac{2x^{1/2}}{x} when simplified?

Why do you think that 3x=x−3 \frac {3}{x} = x^{-3}?

It's been a while since I did indices. I think I have got it sorted now though. I've found a load of practice questions in a video that m4ths/maths247 sent me so I'm going through them now.

Original post by the bear
yes... you are heading in the right direction now :wink:

Thanks for your help :smile:
Reply 13
Avatar for games211
games211
16
Original post by the bear
what Super said. then use the idea

if y = axn

then dy/dx = anxn-1


is it 5-x^-3/2-3x^-2
Reply 14
Avatar for Moonwalker39
Moonwalker39
OP
Original post by games211
is it 5-x^-3/2-3x^-2

That's what I get, so I'm guessing that's correct.

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