Question

find the nth derivative of 2x-1/(x-2)(x+1)​

Answer 1

Answer:

please refer to the attachment

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Answer 2

Answer:

The nth derivative of  $\frac{2x-1}{(x-2)(x+1)}$ is

$y_{n} = [(-1)^{n}n!(n-2)^{-(n+1)} ] + [(-1)^{n}n!(n+1)^{-(n+1)}]$

Step-by-step explanation:

The derivative of the given equation is

$f(x) = \frac{2x-1}{(x-2)(x+1)}\\\\f(x) = y = \frac{1}{x-2} + \frac{1}{x+1}\\\\y_{1} = [-(x-2)^{-2}] + [-(x+1)^{-2}] \\\\y_{2} = [2(x-2)^{-3}] + [2(x+1)^{-3}]\\\\y_{3} = [-3*2(x-2)^{-4}] + [-3*2(x+1)^{-4}]\\\\.\\.\\.\\y_{n} = [(-1)^{n}n! (x-2)^{-(n+1)}] + [(-1)^{n}n! (x+1)^{-(n+1)}]$

Derivative:

In mathematics, a function's derivative is the rate at which it changes in relation to a certain variable. Calculus and differential equations issues must be solved using derivatives in order to be successfully solved.

A function's derivative can be understood as the slope of the function's graph or, more accurately, as the slope of the tangent line at a given point. In actuality, it is calculated using the slope formula for a straight line, with the exception that curves require the application of a limiting procedure. The ratio of the change in y to the change in x, or the slope in Cartesian terms, is a common way to represent the slope. The formula for the slope of the straight line in the illustration is (y1 y0)/(x1 x0).

To learn more about derivatives, click on the link below:

https://brainly.com/question/23819325

To learn more about differential equations, click on the link below:

https://brainly.com/question/1164377

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