Question

i cant figure out the first derivative of this function...1/(5x^2+3).. and help.. i know its the quotient rule but i need some help

Answer 1

think of it this way.. (5x^2+3)^ -1

Answer 2

then you can use the power rule to solve it :)

Answer 3

so to the start its the f'(x)=-5x^2-3?

Answer 4

yup and qiuck question is it - or + 3

Answer 5

im in 4th grade\

Answer 6

the original equation is +... but the derivative i believe would be negative right?//

Answer 7

4th grade huh..freakin genius

Answer 8

-(5x^2 +3) ^ -2
now take the derivitive of the inside function...
{-(5x^2 +3) ^ -2} x {10x}
so the final answer is..
-10x(5x^2 +3)^-2

Answer 9

thanks for that refreshment.. ill keep you in mind when i need help there

Answer 10

no probs. you in hs or college?

Answer 11

college.. you really in 4th?

Answer 12

want to help me with the second derivative of that f'(x)>?

Answer 13

i'm in hs, haha and surely

Answer 14

is that the product rule?

Answer 15

yeah, usually whenever i see something in the denominator i'll make it a negative exponent and solve it that way

Answer 16

ya i totally forgot about that trick

Answer 17

f 'g + g'f
{-(5x^2 +3) ^ -2} x {10} + {20x(5x^2 +3) ^ -3} {10x}
ok so i think that's what it is haha do you agree? i just used the product rule for it then the chain rule to find the derivitive of the ugly function

Answer 18

where did you use the chain rule at>

Answer 19

to find the derivitive of this function: {-(5x^2 +3) ^ -2}

Answer 20

isnt the chain rule for the function -10x(5x^2+3)^-2?

Answer 21

no, because in order to find the f'(x) of {-10x} x {(5x^2+3)^-2} you must assign one to be the g function and the other one the f function.. then you use f'g+g'f

Answer 22

i got (-10)(5x^2+3)^-2 + (-10x)(10x)(20x)(5x^2+3)^-3......before simplifying

Answer 23

what the heck did you do?

Answer 24

that was the first derivative .. and to find the second derivative you have to take the derivative of f'(x)....

Answer 25

so i took the product rule of f'(x).. and the chain rule after ...

Answer 26

no, how did you find the derivitive of -(5x^2 +3) ^ -2

Answer 27

we already established that derivative ...

Answer 28

that was the -10x(5x^2+3)^-2

Answer 29

because for this you need to use the chain rule..
which means you would bring the -2 down and subtract one from the exponent
-(-2)(5x^2 +3) ^-3
then take the derivitive of the inside function..
2(5x^2 +3) ^-3 x (10x)

Answer 30

the equation is different than the orginial part of the problem

Answer 31

unless that was the first derivative the -(5x^2+3)^-2???

Answer 32

ya that was teh first der.

Answer 33

i think

Answer 34

no. pretend it's a new function, don't even think about the first equation...
f(x)={-(5x^2 +3) ^ -2}
g(x)={10x}
Product rule..
f 'g + g'f
{-(5x^2 +3) ^ -2} x {10} + {20x(5x^2 +3) ^ -3} {10x}

Answer 35

i mean.. g'f + f'g

Answer 36

are you following?

Answer 37

yes that all makes sense.. i was considering the exponent "-2" as g(x)..

Answer 38

thats why iw as getting confused ..

Answer 39

no worries :)