How do you differentiate f(x) = sec(x^2 + 1)^2f(x)=sec(x2+1)2?
2 Answers
Explanation:
The derivative of the sec of a function is the sec of the function multiplied by the tan of the function multiplied by the derivative of the function. And the derivative of a function to a power is, by the power rule, the power times the function raised to one less than the given power, times the derivative of the function. And the derivative of a polynomial function is the power times the coefficient times the variable raised to one less than the given power.
Here is the "How" using notation.
Explanation:
= sec(x^2+1)^2tan(x^2+1)^2 * 2(x^2+1)d/dx(x^2+1)
= sec(x^2+1)^2tan(x^2+1)^2 * 2(x^2+1)(2x)
= 4x(x^2+1) sec(x^2+1)^2tan(x^2+1)^2