If y- logsin x- prove that d3ydx3-2 cos x cosec3x-

y=log (sin x) dydx=1 sinx cosx= cotx d^2ydx^2= cosec^2x d^3ydx^3= 2cosec x ( cosec x x) d^3ydx^3=2cos x cosec^3x ...

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If y= logsi...

Question

If $y = log (sin x)$ , prove that $\frac{d^{3} y}{d x^{3}} = 2 cos x {cosec}^{3} x$ .

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y = x^{2} log x

\frac{d^{3} y}{d x^{3}} = \frac{2}{x}

x = a t^{3}

y = b t^{2}

t

\frac{d^{3} y}{d x^{3}} = \frac{8. b}{27 a^{3} . t^{7}}

D \cdot E

{(\frac{d^{3} y}{d x^{3}})}^{\frac{1}{6}} \cdot {(\frac{d y}{d x})}^{\frac{1}{3}} = 5

(\frac{d^{3} y}{d x^{3}}) \cdot {(\frac{d y}{d x})}^{2} = 5^{6}

y = cos (3 {cos}^{- 1} x)

\frac{d^{3} y}{d x^{3}}

x = a {sec}^{2} θ

y = a {tan}^{3} θ

\frac{d^{3} y}{d x^{3}}

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