If y = sin x + cos 3x, find the third derivative of y?

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We have the function y = sin x + cos 3x.

The derivative of sin x is cos x and the derivative of cos x is -sin x.

Also, for a function of the form y= f(g(x)), the derivative of y or y' is given by f'(g(x))*g'(x). This is known as the chain rule.

We use the chain rule and the identities mentioned above to find the third derivative of y = sin x + cos 3x

y' = cos x - 3* sin 3x

y'' = -sin x - 9*cos 3x

y''' = -cos x + 27*sin 3x

The third derivative of y = sin x + cos 3x is -cos x + 27*sin 3x.

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