Question

How do you differentiate `tan(cos^3(x))`?

Answer 1

Use the Chain Rule: `d/dx(tan(cos^3(x)))=sec^2(cos^3(x))\cdot d/dx(cos^3(x))`

`=sec^2(cos^3(x))\cdot 3cos^2(x)\cdot (-sin(x))`

`=-3sin(x)cos^2(x)sec^2(cos^3(x))`