If y = sin³ x find nth term of y

Learn how to find If y = sin³ x find nth term of y. using partial fractions and differentiation techniques. Follow our detailed step-by-step

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

Solution:- Let $y = \sin^3 x$

We know that

$\sin 3x = 3\sin x - 4\sin^3 x$

⇒ $4\sin^3 x = 3\sin x - \sin 3x$

⇒ $\sin^3 x = \frac{1}{4}[3\sin x - \sin 3x]$

Since, $y = \frac{1}{4}[3\sin x - \sin 3x]$

Differentiate with respect to x

$y_1 = \frac{1}{4}[3\cos x - 3\cos 3x]$

⇒ $y_1 = \frac{1}{4}[3\sin(x + \pi/2) - 3\sin(3x + \pi/2)]$

Again differentiate with respect to x

⇒ $y_1 = \frac{1}{4}[3\sin(x + 2\pi/2) - 3^2\sin(3x +2 \pi/2)]$

Now, differentiate this equation for $y_n$

⇒ $y_1 = \frac{1}{4}[3\sin(x + n\pi/2) - 3^n\sin(3x +n \pi/2)]$

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

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

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

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

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

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

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

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

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