1. ## If P=20t+45t^2 find dp/dt - can someone please check my working and answer? :)

New to the subject. Help would be much appreciated

2. ## Re: If P=20t+45t^2 find dp/dt - can someone please check my working and answer? :)

$p=20t + 45 t^2$

$\dfrac{d}{dt} c t^n = c n t^{n-1}$

$\dfrac{dp}{dt}=20 + 90 t$

3. ## Re: If P=20t+45t^2 find dp/dt - can someone please check my working and answer? :)

I presume that you are required here to use the "difference quotient" definition. That is that the derivative is defined as $\lim_{dx\to 0} \frac{P(t+ dt)- P(t)}{dx}$ (Many people do not like using "dt" here, reserving that for after the limit). Yes, with $P(t)= 20t+ 45t^2$, $P(t+ dt)= 20(t+ dt)+ 45(t+ dt)^2$.

But then you have an error in your very next line. You have 20(t+ dt) equal to 20t+ dt. It should be 20t+ 20dt. So $P(t+ dt)= 20t+ 20dt+ 45t^2+ 90t dt+ dt^2$

And subtracting $P(t)= 20t+ 45t^2$ from that leaves $P(t+ dt)- P(t)= 20dt+ 90 t dt+ dt^2$. You have only "dt" rather than "20dt". Finally, dividing by "dt", $\frac{P(t+dt)- P(t)}{dt}= 20+ 90t+ dt$ and the limit of that as dt goes to 0 is 20+ 90t.

4. ## Re: If P=20t+45t^2 find dp/dt - can someone please check my working and answer? :)

As your Q. stands, there is not a specific & stated requirement to use the "difference quotient" definition. Hence, the solution provided in post #2 is adequate. Although the solution given in post #3 is mathematically valid, it is based on an unjustified presumption and is akin to using a sledge hammer to crack a nut.

Al.

5. ## Re: If P=20t+45t^2 find dp/dt - can someone please check my working and answer? :)

Originally Posted by Skywave
As your Q. stands, there is not a specific & stated requirement to use the "difference quotient" definition. Hence, the solution provided in post #2 is adequate. Although the solution given in post #3 is mathematically valid, it is based on an unjustified presumption and is akin to using a sledge hammer to crack a nut.

Al.
The student's attempt to do the problem is, in fact, your sledge hammer. And as this is likely the start of a summer course it's probably the only method (s)he knows.

-Dan

6. ## Re: If P=20t+45t^2 find dp/dt - can someone please check my working and answer? :)

Originally Posted by topsquark
The student's attempt to do the problem is, in fact, your sledge hammer.
And as this is likely the start of a summer course it's probably the only method (s)he knows.
-Dan
Your first sentence carries no logic at all!
And your second sentence needs to be proven, before it can claimed to be valid!

Al. / Skywave

7. ## Re: If P=20t+45t^2 find dp/dt - can someone please check my working and answer? :)

Thanks for the help everyone guess I made a mistake. I've since learned the power rule for differentiation which is much easier. I should have looked into that earlier.