4/ 3\ sec \x /
d / 4/ 3\\ --\sec \x // dx
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 :
Let .
The derivative of cosine is negative sine:
Then, apply the chain rule. Multiply by :
Apply the power rule: goes to
The result of the chain rule is:
The result of the chain rule is:
The result of the chain rule is:
Now simplify:
The answer is:
2 4/ 3\ / 3\ 12*x *sec \x /*tan\x /
4/ 3\ / / 3\ 3 / 2/ 3\\ 3 2/ 3\\ 12*x*sec \x /*\2*tan\x / + 3*x *\1 + tan \x // + 12*x *tan \x //
4/ 3\ / 3 / 2/ 3\\ 3 2/ 3\ 6 3/ 3\ 6 / 2/ 3\\ / 3\ / 3\\ 24*sec \x /*\9*x *\1 + tan \x // + 36*x *tan \x / + 72*x *tan \x / + 63*x *\1 + tan \x //*tan\x / + tan\x //