Calculus- Chain,product or quotient rule?

[maali5]

Hi, teachers

I have been doing some work but I am confused.

Have you ever heard of this great math website www.wolframalpha.com (Google for maths).

This is one questions I done differantiate 3e^-4tsin(5t) and here is the link for the answers from

http://www.wolframalpha.com/input/?i=differantiate++3e^-4tsin(5t)


Although what I did is confusing to what the answers there?

This my solution

y=3e^-4t sin(5t)

u=3e^-4t v =sin(5t)

dy/dt=-12e^-4t dv/dt=-5cos(5t)


chain rule/product rule (1 of them)

ds/dt= 3e^-4t x 5cos(5t) + sin(5t) x -12e^-4t

factor

=3e^-4t (5cos(5t) - 4sin (5t))

Am I or the computer correct

 

[Deleted member 4993]

Hi, teachers

I have been doing some work but I am confused.

Have you ever heard of this great math website www.wolframalpha.com (Google for maths).

This is one questions I done differantiate 3e^-4tsin(5t) and here is the link for the answers from

http://www.wolframalpha.com/input/?i=differantiate++3e^-4tsin(5t)


Although what I did is confusing to what the answers there?

This my solution

y=3e^-4t sin(5t)

u=3e^-4t v =sin(5t)

dy/dt=-12e^-4t dv/dt= -5cos(5t) <<< That is incorrect; it should be → d(sin5t)/dt = 5cos(5t)


chain rule/product rule (1 of them)

ds/dt= 3e^-4t x 5cos(5t) + sin(5t) x -12e^-4t

factor

=3e^-4t (5cos(5t) - 4sin (5t))

Am I or the computer correct

.

 

[maali5]

.

:idea:

So, who is right? me vs computer

Forgive me by asking so many questions


Also while you there can you look at the following two question that I have.


1) The table gives a firm’s monthly profits for their first few months of business. The numbers are rounded to the nearest £100.

Number of months after start up (x)	1	2	3	4	5	6
Profit for this month (£y)	500	800	1200	1900	3000	4800

The firm’s profits, £y, for the x^th month after start up are modelled by

y = k x 10^ax

where a and k are constants.

Plot this data on semi log paper to verify if this relationship is true.

Its about plotting semi-log paper but am confused. Can you give me guide on where to start answering the question.

Thanx agin



2)
Simultaneos question

y = x² – 5x + 5 a



5x + 3y = 30. b​

​

Find location of points collide?


Add a+b

x² + 2y -25=0


quadratic formula use

x= -2+ square root(2^2-(4x1x(-25))/2 x = 4.09901

or

x= -2 - square root(2^2-(4x1x(-25))/2 x=-6.09


subsitue y etc


Wrong or right?

 

[pka]

So, who is right? me vs computer

The correct answer is:
\(\displaystyle 15e^{-4t}\cos(5t)-12e^{-4t}\sin(5t)~.\)

You must input correctly.