Question

if y(x)=1/3cos^34x,then dy/dx is​

Answer 1

Answer:

$\frac{dy}{dx}=-4\cos^{2}  4x \sin4x$

Step-by-step explanation:

We have $y=f(x)=\frac{1}{3} \cos^{3} 4x$ and we have to find $\frac{dy}{dx}$

Now, $y=f(x)=\frac{1}{3} \cos^{3} 4x$  

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

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

⇒ $\frac{dy}{dx}=-4\cos^{2}  4x \sin4x$ ( Answer )