anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
think of it this way.. (5x^2+3)^ -1
anonymous
  • anonymous
then you can use the power rule to solve it :)
anonymous
  • anonymous
so to the start its the f'(x)=-5x^2-3?

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anonymous
  • anonymous
yup and qiuck question is it - or + 3
anonymous
  • anonymous
im in 4th grade\
anonymous
  • anonymous
the original equation is +... but the derivative i believe would be negative right?//
anonymous
  • anonymous
4th grade huh..freakin genius
anonymous
  • 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
  • anonymous
thanks for that refreshment.. ill keep you in mind when i need help there
anonymous
  • anonymous
no probs. you in hs or college?
anonymous
  • anonymous
college.. you really in 4th?
anonymous
  • anonymous
want to help me with the second derivative of that f'(x)>?
anonymous
  • anonymous
i'm in hs, haha and surely
anonymous
  • anonymous
is that the product rule?
anonymous
  • anonymous
yeah, usually whenever i see something in the denominator i'll make it a negative exponent and solve it that way
anonymous
  • anonymous
ya i totally forgot about that trick
anonymous
  • 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
  • anonymous
where did you use the chain rule at>
anonymous
  • anonymous
to find the derivitive of this function: {-(5x^2 +3) ^ -2}
anonymous
  • anonymous
isnt the chain rule for the function -10x(5x^2+3)^-2?
anonymous
  • 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
  • anonymous
i got (-10)(5x^2+3)^-2 + (-10x)(10x)(20x)(5x^2+3)^-3......before simplifying
anonymous
  • anonymous
what the heck did you do?
anonymous
  • anonymous
that was the first derivative .. and to find the second derivative you have to take the derivative of f'(x)....
anonymous
  • anonymous
so i took the product rule of f'(x).. and the chain rule after ...
anonymous
  • anonymous
no, how did you find the derivitive of -(5x^2 +3) ^ -2
anonymous
  • anonymous
we already established that derivative ...
anonymous
  • anonymous
that was the -10x(5x^2+3)^-2
anonymous
  • 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
  • anonymous
the equation is different than the orginial part of the problem
anonymous
  • anonymous
unless that was the first derivative the -(5x^2+3)^-2???
anonymous
  • anonymous
ya that was teh first der.
anonymous
  • anonymous
i think
anonymous
  • 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
  • anonymous
i mean.. g'f + f'g
anonymous
  • anonymous
are you following?
anonymous
  • anonymous
yes that all makes sense.. i was considering the exponent "-2" as g(x)..
anonymous
  • anonymous
thats why iw as getting confused ..
anonymous
  • anonymous
no worries :)

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