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

- anonymous

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- anonymous

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

- anonymous

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

- anonymous

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

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- anonymous

yup and qiuck question is it - or + 3

- anonymous

im in 4th grade\

- anonymous

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

- anonymous

4th grade huh..freakin genius

- anonymous

-(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

- anonymous

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

- anonymous

no probs. you in hs or college?

- anonymous

college.. you really in 4th?

- anonymous

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

- anonymous

i'm in hs, haha and surely

- anonymous

is that the product rule?

- anonymous

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

- anonymous

ya i totally forgot about that trick

- anonymous

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

- anonymous

where did you use the chain rule at>

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

what the heck did you do?

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

we already established that derivative ...

- anonymous

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

- anonymous

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)

- anonymous

the equation is different than the orginial part of the problem

- anonymous

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

- anonymous

ya that was teh first der.

- anonymous

i think

- anonymous

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}

- anonymous

i mean.. g'f + f'g

- anonymous

are you following?

- anonymous

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

- anonymous

thats why iw as getting confused ..

- anonymous

no worries :)

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