Question

1)f(x)=2x^(4x)


2)f(x)=4^xlog(small 7)(x)


3)f(x)=[Inx]^4

4)f(x)=In(sqrt(6x+7)(7x-3))

5)f(x)=5cos(7In(x))

6(f(x)=x^2(x-7)^5/(x^2+6)^2

f(x)'=

Answer 1

@mathsmind

Answer 2

this is homework due tomorrow and i am stuck!

Answer 3

well they are all simple i can solve them in my head, but let me show u how to do them

Answer 4

Thank you so much, thats graceful

Answer 5

solving for Q1
\[f(x)=2x^{4x}\]

Answer 6

step one: take the natural log of both sides, i will define f(x) as being y ok

Answer 7

ok,

Answer 8

\[\ln[y=2x^{4x}] \longrightarrow lny= \ln2x^{4x}\]

Answer 9

clear so far

Answer 10

\[ lny= 4x(\ln2x)\]

Answer 11

now we will be using the product rule

Answer 12

for the right hand?

Answer 13

yes

Answer 14

D(lny)=1/y

Answer 15

left is 1/y
right is 4x(1/2x)+(In2x)(4)

Answer 16

d(4x(ln2x))= 4ln(2x)=2x^4x(4ln(x)+4)

Answer 17

=y(2x^4x(4ln(x)+4))

Answer 18

but we know that y = to the main function

Answer 19

=2x^(4x)(2x^4x(4ln(x)+4))

Answer 20

that's the end of q1

Answer 21

f(x)=4^xlog(small 7)(x)

Answer 22

u mean to the base 7 right?

Answer 23

yes,

Answer 24

the answer for the first question is \[f(x)= 2x^4(2x^{4x})(4In(x)+4)? \]

Answer 25

no

Answer 26

could you write it down by using Equation bottom?

Answer 27

thanks for your patience.

Answer 28

\[2x^{4x}(4\ln(x)+4)\]

Answer 29

i entered it but it says In is not defined

Answer 30

entered what?

Answer 31

the answer 2x^(4x)(4In(x)+4)

Answer 32

yes that is exactly what i did

Answer 33

undefined because it can't read latex prbably

Answer 34

probably*

Answer 35

\[2x^{4x}(4\ln(x)+4)\]

Answer 36

yes prob, how do i calculate In(x)?

Answer 37

keep it as it is

Answer 38

ok

Answer 39

I want to know why it wont accpet the answer!

Answer 40

could you help me with the next one

Answer 41

if u are submitting ur answer via a text box in a form then write it exactly in the format they ask u to write it in

Answer 42

look i will solve the problem on a piece of paper and give u the answers ok

Answer 43

Thank you soooo much for helping out here

Answer 44

2)f(x)=4^xlog(small 7)(x)

Answer 45

\[y=4^x \log_{7} (x)\]
please confirm

Answer 46

Yes thats right

Answer 47

\[= \frac{2\ln(2)4^xln(x)}{\ln(7)}+\frac{4^x}{xln(7)}\]

Answer 48

i am sorry for rushing this up because there are others waiting for an answer for their problems...

Answer 49

3)f(x)=[Inx]^4

Answer 50

\[=\frac{4\ln(x)^3}{x}\]

Answer 51

its okay thank you im writing the notes what you have just said

Answer 52

4)f(x)=In(sqrt(6x+7)(7x-3))

Answer 53

=(1/2)*(6/(7*x-3)-(7*(6*x+7))/(7*x-3)^2)*(7*x-3)/(6*x+7) for Q4)

Answer 54

f(x)=5cos(7In(x))

Answer 55

could you use equation bottom for num 4?

Answer 56

f'(x)= -35*sin(7*ln(x))/x

Answer 57

for #4 i got everything divided by 6x+7

Answer 58

6(f(x)=x^2(x-7)^5/(x^2+6)^2

Answer 59

\[f(x)=\frac{x^2(x-7)^5}{(x^2+6)^2}\]

Answer 60

please confirm

Answer 61

Q6

Answer 62

yes

Answer 63

2*x*(x-7)^5/(x^2+6)^2+5*x^2*(x-7)^4/(x^2+6)^2-4*x^3*(x-7)^5/(x^2+6)^3

Answer 64

man that was a long one hehehehe

Answer 65

end wow! fin done no more questions for today hehehe

Answer 66

for this i will give u a medal they are useful derivatives

Answer 67

thank you so much/
wow it is wrong answer!

Answer 68

no it is not the wrong answer hehehehe

Answer 69

show ur work to ur teacher on the piece of paper, and see what she says

Answer 70

i mean long haha. one more thing, in the end it says x^2+6)^3 it should be power 2?

Answer 71

= ((x-7)^4 x (3 x^3+14 x^2+42 x-84))/(x^2+6)^3

Answer 72

i simplified the answer for u

Answer 73

it doesn't matter because u can solve this in different ways, and simplify both answers i gave u are the same

Answer 74

i am 100% sure my answers are correct so its up to u

Answer 75

((x-7)^4 x (3 x^3+14 x^2+42 x-84))/(x^2+6)^3
id it 4x or 4 times?

Answer 76

there is no 4x its to x-7 to the power 4