Question

Question #910e9

Answer 1

`8sec^2(x)tan^3(x)+8sec^4(x)tan(x)`

Explanation:

Here, we'll have to use the Chain Rule, Product Rule, and rules for differentiating trigonometric functions. Let's factor out the constant so the differentiation process is much cleaner:

`4d/dx(sec^2(x)tan^2(x))`

Using the product rule, we get:

`4(d/dx(sec^2(x))tan^2(x)+sec^2(x)d/dxtan^2(x))`

`d/dxsec^2(x)=2sec(x)*d/dxsec(x)=2sec(x)sec(x)tan(x)`

`d/dxtan^2(x)=2tan(x)d/dxtan(x)=2tan(x)sec^2(x)`

Plugging in the above derivatives, our solution becomes:

`4(2sec(x)sec(x)tan(x)tan^2(x)+sec^2(x)2tan(x)sec^2(x))`

Simplifying, we get:

`4(2sec^2(x)tan^3(x)+2sec^4(x)tan(x))`

`8sec^2(x)tan^3(x)+8sec^4(x)tan(x)`