Find nth derivative of the function 1+x/1-x

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Learn how to Find nth derivative of the function 1+x/1-x using partial fractions and differentiation techniques. Follow our detailed step-by-step solution to master this calculus problem

Q 7:- Find nth derivative of the function \dfrac{1-x}{1+x}.

Solution:- Let y = \dfrac{1-x}{1+x}

Differentiate with repect to x

y_1 = \dfrac{d}{dx}.\dfrac{1-x}{1+x}

⇒ y_1 = \dfrac{(1+x)(-1} - (1-x)(1){(1+x)^2}

⇒ y_1 = \dfrac{-1 - x -1 +x}{(1+x)^2}

⇒ y_1 = \dfrac{-2}{(1+x)^2}

⇒ y_1 = -2.(1+x)^{-2}

Again differentiate with respect to x

y_2 = (-2)[-2.(1+x)^{-3}]

⇒ y_2 = 2(-1)^2.(2)!(x + 1)^{-3}

Now differentiate for y_n

y_n = 2(-1)^n.(n)!(x + 1)^{-n-1}

⇒ y_n = \dfrac{2(-1)^n.(n)!}{(x + 1)^{n+1}}

Some other question

Q 1:  If y = \dfrac{x^2}{(x-1)^2(x+2)}, find nth derivative of y.

Solution: See full solution

Q 2: Find the nth derivative of \dfrac{x^2}{(x-a)(x-b)}.

Solution:- See full solution

Q 3:- Find the nth derivative of \tan^{-1}\left[\dfrac{1+x}{1-x}\right]

Solution:- See full solution

Q 4:-  If y = sin³ x find nth term of y.

Solution:- See full solution

Q 5:- Find nth derivative of \tan^{-1}(x/a) .

Solution:- See full solution

Q 6:- Find nth derivative of e^x.x .

Solution:- See full solution

Q 8:- Find nth derivative of \lox x^2

Solution:- Find full solution

Q 9:- Find nth derivative of the funcrtion e^x.\sin^2 x.

Solution:- See full solution

Q 10:- Find the value of nth derivative of y=\cos x\cos 2x \cos 3x.

Solution:- See full solution

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