Question

By Using Chain Rule, find the derivative of

Answer 1

please see the attached file

Answer 2

huh..lets convert the function as (x^3-secx)^1/2

Answer 3

might i make a small suggestion?
since \(\sqrt{x}\) is an amazingly common function, it might do to remember that
\[\frac{d}{dx}[\sqrt{x}]=\frac{1}{2\sqrt{x}}\] and so by the chain rule
\[\frac{d}{dx}[\sqrt{f(x)}]=\frac{f'(x)}{2\sqrt{f(x)}}\] now you do not have to reinvent the wheel every time

Answer 4

yeah sir i guess dats much better....and is it me or my answer is deleted?

Answer 5

looks like it but i don't know why, because it looked right to me

Answer 6

hmm technical problems i guess.

Answer 7

@sara-ali you got this?

Answer 8

you should go right to the answer
\[\frac{f'(x)}{2\sqrt{f(x)}}=\frac{3x^2-\sec(x)\tan(x)}{2\sqrt{x^3-\sec(x)}}\]

Answer 9

no I didnt got this, please explain it further

Answer 10

I don't know how to take derivative

Answer 11

derivative of root x is one over two root x
in notation
\[\frac{d}{dx}[\sqrt{x}]=\frac{1}{2\sqrt{x}}\]

Answer 12

but the question is to find the derivative, right?

Answer 13

so you have to know some derivatives in order to continue

you have to know that the derivative of \(x^3\) is \(3x^2\) for example
also that the derivative of \(\sec(x)\) is \(\sec(x)\tan(x)\) right?

we have so start somewhere

Answer 14

yes I have to find the derivative using chain rule of the attached image. Can you help me to understand this concpt please

Answer 15

yes
do you know what the derivative of \(\sqrt{x}\) is?

Answer 16

no

Answer 17

i guess you have to tell the whole diiferentiation concept @satellite73

Answer 18

you cannot begin to solve the problem without knowing it
the derivative of \(\sqrt{x}\) is \(\frac{1}{2\sqrt{x}}\)
i.e.
\[\frac{d}{dx}[\sqrt{x}]=\frac{1}{2\sqrt{x}}\] we have to know this to start the problem

Answer 19

do you know what the derivative of \(x^3\) is?

Answer 20

1 / 2sqrx^3 right?

Answer 21

@fortheloveofscience i cannot do it here. that is why calc class meets for a whole semester

Answer 22

no the derivative of \(x^3\) is \(3x^2\)

Answer 23

but how do we find it ?

Answer 24

I only know the forumla of finding slope of tangent and sec line

Answer 25

you can find it using the so called "power rule" i.e.
\[\frac{d}{dx}[x^n]=nx^{n-1}\]

Answer 26

you also need to know what the derivative of \(\sec(x)\) is
do you know that one?

Answer 27

No, I don't know please help me

Answer 28

so you have a text book? for these you have to memorize them or use notes, you will not compute it by hand

Answer 29

can you tell me please good websites where I can easily understand the concept of derivative?

Answer 30

http://people.ucsc.edu/~miglior/diffform.pdf
maybe this link wld help @sara-ali

Answer 31

calculus is not really that easy, especially not the first time you see it. this is a fairly advanced question at the introductory level and cannot be done without some knowledge of derivatives.
i am sure all the information is in your text book

Answer 32

Please after this question @satellite73 see my maths question @maheshmeghwal9

Answer 33

in order to do this question you need to have at your fingertips three derivatives:
the derivative of \(x^3\) is \(3x^2\)
the derivative of \(\sec(x)\) us \(\sec(x)\tan(x)\)
the derivative of \(\sqrt{x}\) is \(\frac{1}{2\sqrt{x}}\)

you also need to know some rules about combining derivatives
\[(f+g)'=f'+g'\] and also
\[(f(g))'=f'(g)g'\] so there is a lot packed in to this one question

Answer 34

Thanks for your help and time @satellite73 .. .