Question

If y(x)=1/3cos^34x,then dy/dx is​

Answer 1

`(dy)/(dx)=-4\cos^(2)  4x \sin4x`

Explanation:

We have
`y=f(x)=(1)/(3) \cos^(3) 4x` and we have to find
`(dy)/(dx)`

Now,
`y=f(x)=(1)/(3) \cos^(3) 4x`

Differentiating both sides of the equation with respect to x we get,

`(dy)/(dx) = (1)/(3) * 3 * \cos^(2) 4x * (-\sin4x) * 4` {Since we know the formula
`(dx^(n) )/(dx) =nx^(n-1)` and another formula
`(d(\cos x))/(dx) = -\sin x`}

⇒
`(dy)/(dx)=-4\cos^(2)  4x \sin4x` ( Answer )