Question

I have the answer can someone please check me ...
Find the derivative
m(t)=(5)cos^2t

Answer 1

\[5\cos^2(t)\]?

Answer 2

The equation for the question is \[m(t)=\frac{ 5 }{ \cos^2t }\]

Answer 3

\[5\sec^2(t)\]?

Answer 4

it will be \(10\sec(t)\times \frac{d}{dx}\sec(t)\) or
\[10\sec(t)\sec(t)\tan(t)\] or even
\[10\sec^2(t)\tan(t)\]

Answer 5

could the answer be\[m'(t)=\frac{ 5 }{ 2sint cost }\]

Answer 6

no

Answer 7

it is easiest to turn in to \(5\sec^2(t)\) but if for some reason you want to work with \(\frac{5}{\cos^2(t)}\) you have to either use the quotient rule or the rule for reciprocals.
i would make life easy and rewrite as \(5\sec^2(t)\) as a first step

Answer 8

you cannot take the derivative of the denominator to solve this

Answer 9

just like the derivative of \(\frac{5}{x^2}\) is not \(\frac{5}{2x}\)

Answer 10

ok but all of these answers you are saying are not any of my multiple choice answers

Answer 11

\[\frac{d}{dt}m(t)=\frac{d(5\sec^2 t)}{dt}=5\frac{d\sec^2 t}{d\sec t}\frac{d\sec t}{dt}=10\sec^2 t \tan x\]

Answer 12

I have\[\frac{ 10\sin t }{ \cos^3 t }\]

Answer 13

First of all, I have a typo lol.

Secondly, \[\frac{10\sin t}{\cos^3 t}=10\frac{\sin t}{\cos t}\frac{1}{\cos^2 t}=10\tan t \sec^2 t\]

Answer 14

I am getting really confused so would the answer I just gave be correct

Answer 15

You can try to manipulate the answer you have.

Answer 16

would \[\frac{ 10 \sin t }{ \cos t}\]

Answer 17

is that a better answer

Answer 18

\[\frac{10\sin t}{\cos t}\neq \frac{10 \sin t}{\cos^3 t}=10\tan t \sec^2 t\]

Answer 19

um I don't have that for one of my choices

Answer 20

What choices do you have?

Answer 21

I have\[\frac{ -10 \sin t }{ \cos^3 t }\]

Answer 22

I have\[\frac{ 10 \sin t }{ \cos^3 t }\]

Answer 23

I have \[\frac{ 10 \sin t }{ \cos t }\]

Answer 24

I have \[\frac{ 5 }{ 2sint \cos t }\]

Answer 25

I have \[\frac{ -5 }{ 2\sin t \cos t }\]

Answer 26

I have 5tant

Answer 27

I have \[\frac{ -10 \sin t }{ \cos t }\]

Answer 28

and I have -5tan t

Answer 29

Those are all of my choices that I have

Answer 30

Do you miss out a negative sign in the question?

Answer 31

no negative in the question

Answer 32

Can anyone help me please

Answer 33

@farmergirl411 did you get the answer?

Answer 34

no I am reallly stuck what I thought was the answer everyone told me it was not. I have multiple choice answers. If you scroll up a bit every post where I said I have, I have is a multiple choice answer I to choose from

Answer 35

I saw your question. I'll try to help you :)

Answer 36

ok thanks you so much:)

Answer 37

\[m(t)=\frac{5}{\cos^2 t}\]
We know that
\[\frac 1 {\cos t} =\sec t\]
so
\[m(t)=5 \sec^2 t\]
Let's take the derivative of this
\[m'(t)=5\times 2 \times {\sec^{2-1} t}\times \sec t\times \tan t\]
we'd get
\[m'(t)=10\sec^2 t\times \tan t\]
Do you get till here?

Answer 38

yes

Answer 39

\[m'(t)=10\times \frac 1 {\cos^2 t}\times \frac{\sin t}{\cos t}\]
We get finally
\[m'(t)=10\times \frac{\sin t}{\cos^3 t}\]

Answer 40

I think it does match one of your option, doesn't it?

Answer 41

yes it does only can I put 10 next to the sint then it will match a choice

Answer 42

yes :)

Answer 43

awesome thaank you sooooooooo much:)