Mistakes give rise to Problems- 15

Calculus Level 2

If you are given a function $\color{#69047E}{y= 19x^4-13x^3+11x^2-7x+5}$ then we can do it's differentiation as $\color{#3D99F6}{\dfrac{\textbf{dy}}{\textbf{dx}} = 76x^3-39x^2+22x-7}$

If you are given that $y=13x^3-12x^2+11x-10$ then find the answer of $\color{#D61F06}{\dfrac{\textbf{dy}}{\textbf{dt}}}$

Details and Assumptions

$t$ is not a monic linear function of $x$ .

This problem is a part of the set Mistakes give rise to problems

None of these

39x^2-24x+11

39x^2+24x-11

39x^3+24x^2+11x-10

1 solution

Aditya Raut
Aug 15, 2014

See that the asked differentiation is in terms of $t$ , and $y$ is a function of $x$ .

Thus the answer of the question is as follows,

$\dfrac{dy}{dt} = \dfrac{dy}{dx} \cdot \dfrac{dx}{dt}$

Hence asked thing is $\dfrac{dy}{dt} =( 39x^2-24x+11) \dfrac{dx}{dt}$

And as $t$ is not a monic linear function of $x$ , the value of $\dfrac{dx}{dt}$ is NOT 1.

Hence the answer is $( 39x^2-24x+11) \dfrac{dx}{dt}$ which is not in the options, giving $\boxed{\text{None of these}}$ as the correct answer.

I thought since there is no given relation between x and t hence

$\frac{dx}{dt}=0$ Still I got the right answer.

Ronak Agarwal - 6 years, 10 months ago

This is not necessary buddy, I only gave that $t$ is not monic function of $x$ . This never meant that $\dfrac{dx}{dt}=0$ , that was a trap and luckily your thing worked.

Aditya Raut - 6 years, 10 months ago

You should try this problem : Let's play pool . I'm sure you will like it.

Ronak Agarwal - 6 years, 10 months ago

@Ronak Agarwal – Good, I suggest you some edits in the LaTeX of the problem.

For the symbol of belongs to , do not use \epsilon .

\epsilon will appear as $\epsilon$ , the code for belongs to is \in

\in appears as $\in$

So write it as

y \in (c,d)

which will give output $y \in (c,d)$

Aditya Raut - 6 years, 10 months ago

I misread it as t _is _ a monic function of x.. SHIT!

Pankaj Joshi - 6 years, 9 months ago

Well , that's how i did it.

Keshav Tiwari - 6 years, 10 months ago

Mistakes give rise to Problems- 15

This problem is a part of the set Mistakes give rise to problems

1 solution

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