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