Question #910e9

1 Answer
VNVDVI
Feb 23, 2018

#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)#

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