Question

y = cosec^3 (3x+3) find dy/dx

Answer 1

Step-by-step explanation:

Explanation:

We can rewrite y=csc3(x) as y=(cscx)3.

Using the Power rule and chain rule, we get

y'=3(cscx)2⋅ddx(cscx)=3csc2(x)⋅−csc(x)cot(x)=−3csc3(x)cot(x)

As ddxcsc(x)=−csc(x)cot(x).

Here's a proof of this derivative:

csc(x)=1sin(x)=(sinx)−1

Since ddxsin(x)=cos(x), using the Power Rule and Chain Rule on ddx(sinx)−1 yields

ddx(sinx)−1=−(sinx)