Question

find the following derivatives:

1. d/dx (squareroot of xe^x)

and

2. d/dx ( e^x / cos x)

Answer 1

for the first one, apply the rule for the derivative of a product of functions.
for the second one, it's the formula of a quotient.
These formulas exist, so just apply.

Answer 2

not really sure what that means....

Answer 3

im completely lost on this question

Answer 4

\((f(x)\times g(x))' = f'(x)g(x) + f(x)g'(x)\).

Answer 5

in 1., you have the product of the function \(x\) with the function \(e^x\).
apply the formula: \((xe^x)' = x' e^x + x(e^x)'\). Do you see that I just appied the formula?

Answer 6

applied*

all you need to do after writing applying the formula is to compute the derivatives that need to be computed (easy).

Answer 7

do you have the answer for question 1. ?

Answer 8

no

Answer 9

I was almost at the end:
\(x'e^x = x(e^x)' = 1e^x+x(e^x) = e^x(1+x)\) .

Answer 10

i just dont get how you got that its gibberish to me. ugh

Answer 11

There is formula (that you must apply here) that explains how to compute the derivative of a product of functions. It is: \((fg)'=f'g+fg'\). Is it ok until here?

Answer 12

ok

Answer 13

I didn't see the word "squareroot" .. ouch.

do you know how to compute : \((\sqrt{x})'\) ?

Answer 14

multiply the reciprocal?

Answer 15

?

Answer 16

no i do not

Answer 17

one (more) formula to remember: \((x^\alpha)' = \alpha x^{\alpha-1}\)
so: \((\sqrt x)' = (x^{1/2})' = \frac12x^{-1/2}\).

Answer 18

there are formulas for product, quotient, and composition of functions.
- product: i wrote it above
- quotient: \((\frac{f}{g})' = \frac{gf'-fg'}{g^2}\)
- composition: \((f(g(x)))' = f'g(x))g'(x)\).

Answer 19

1. is \(\sqrt{xe^x}\) if I'm not wrong. Here, it's tricky. there is a product of functions, and there is a composition of functions.
You must see put some parts in a box "B".. here let's put \(B=xe^x\), and we see that your function is actually \(\sqrt{B}\).

Answer 20

by the formula for compound functions, \((\sqrt{B})' = \frac{1}{2}B^{-1/2} \times B'\).
Then the formula for a product of functions helps yo uto compute \(B'\).

Answer 21

- composition \((f(g(x)))′=f′(g(x))g′(x).\)
(i forgot one parenthesis "(" )

Answer 22

is it a bit clearer?

Answer 23

no im just going to have to go back to book and figure it out but thank you so much!

Answer 24

start with products, then go for compound, then, 1.

Answer 25

one last question if i can... for this problem i think its undefined but not sure...