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Higher Order Derivatives

If y=cos 2 ...

Question

If $y = {cos}^{2} \frac{3 x}{2} - {sin}^{2} \frac{3 x}{2}$ , then $\frac{d^{2} y}{{d x}^{2}}$ is

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Solution

$y = {cos}^{2} \frac{3 x}{2} - {sin}^{2} \frac{3 x}{2} = cos (2 \times \frac{3 x}{2}) = cos 3 x \frac{d y}{d x} = - 3 sin 3 x \frac{d^{2} y}{d x^{2}} = - 9 cos 3 x = - 9 y$

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Similar questions

y = {cos}^{2} \frac{3 x}{2} - {sin}^{2} \frac{3 x}{2}

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

x = 2 {a t}^{2}, y = {a t}^{4}

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

t = 2

y = \frac{1}{2 x^{2} + 3 x + 1}

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

x = - 2

x = a t^{2}

y = 2 a t

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

t = 2

y = \frac{1}{2 x^{2} + 3 x + 1}

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

x = - 2

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