How do you differentiate f(x)=sec^4(e^(x^3) ) using the chain rule?
1 Answer
Jan 28, 2016
Explanation:
The first issue is the fourth power. We can deal with it through the application of the chain rule
f'(x)=4sec^3(e^(x^3))*d/dx(sec(e^(x^3)))
To differentiate the secant function, use the rule:
f'(x)=4sec^3(e^(x^3))sec(e^(x^3))tan(e^(x^3))*d/dx(e^(x^3))
Which simplifies to be
f'(x)=4sec^4(e^(x^3))tan(e^(x^3))*d/dx(e^(x^3))
All that remains is the differentiation of
f'(x)=4sec^4(e^(x^3))tan(e^(x^3))*e^(x^3)d/dx(x^3)
Since
f'(x)=12x^2e^(x^3)sec^4(e^(x^3))tan(e^(x^3))