2 sec (x) - 2*tan(x)
sec(x)^2 - 2*tan(x)
Differentiate term by term:
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
Rewrite the function to be differentiated:
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
The derivative of cosine is negative sine:
The result of the chain rule is:
The result of the chain rule is:
The derivative of a constant times a function is the constant times the derivative of the function.
Rewrite the function to be differentiated:
Apply the quotient rule, which is:
and .
To find :
The derivative of sine is cosine:
To find :
The derivative of cosine is negative sine:
Now plug in to the quotient rule:
So, the result is:
The result is:
Now simplify:
The answer is:
2 2 -2 - 2*tan (x) + 2*sec (x)*tan(x)
/ 2 / 2 \ / 2 \ 2 2 \ 2*\sec (x)*\1 + tan (x)/ - 2*\1 + tan (x)/*tan(x) + 2*sec (x)*tan (x)/
/ 2 \ | / 2 \ 2 / 2 \ 2 3 2 / 2 \ | 4*\- \1 + tan (x)/ - 2*tan (x)*\1 + tan (x)/ + 2*sec (x)*tan (x) + 4*sec (x)*\1 + tan (x)/*tan(x)/