Find the derivative of (x+3)/(2x-5)
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calendarEducator since 2010
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We have to find the derivative of (x+3)/(2x-5).
This can be done using the product rule which states that the derivative of h(x) = f(x)* g(x) = f'(x)*g(x) + f(x)*g'(x) and the chain rule
Take the given expression (x+3)/(2x-5)
= (x+3)*(2x - 5)^-1
The derivative is (x +3)*(-1)*2*(2x - 5)^-2 + 1*(2x - 5)^-1
=> -2(x + 3)/ (2x - 5)^2 + 1/ (2x - 5)
=> [-2x - 6 + 2x - 5]/ (2x - 5)^2
=> -11 / (2x - 5)^2
The required result is -11 / (2x - 5)^2
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calendarEducator since 2008
write3,662 answers
starTop subjects are Math, Science, and Social Sciences
Let f(x) = (x+3)/(2x-5)
We will use the quotient rule to find the derivative.
We will assume that f(x) = u/v such that:
u= x+3 ==> u' = 1
v = 2x-5 ==> v' = 2
==> Then, we know that f'(x) = (u'v- uv')/v^2
==> f'(x) = (1*(2x-5) - (x+3)(2)]/ (2x-5)^2
==> f'(x) = ( 2x-5 - 2x -6)/ (2x-5)^2
= ( -11/ (2x-5)^2
==> f'(x) = -11/(2x-5)^2