sec(x) derivative
To find the derivative of the sec(x) function, we will use the rules of calculus
To find the derivative of the sec(x) function, we will use the rules of calculus.
First, let’s clarify that the sec(x) function can also be written as 1/cos(x).
To find the derivative of sec(x), we can use the quotient rule, which states that if we have a function of the form f(x) = g(x)/h(x), then its derivative is given by:
f'(x) = (g'(x) * h(x) – g(x) * h'(x)) / (h(x))^2
In our case, g(x) is 1 and h(x) is cos(x). Therefore, g'(x) is 0 and h'(x) is -sin(x).
Plugging these values into the quotient rule formula, we get:
f'(x) = (0 * cos(x) – 1 * (-sin(x))) / (cos(x))^2
= sin(x) / cos^2(x)
Now, we can simplify further. Dividing sin(x) by cos^2(x) is equivalent to multiplying sin(x) by (1 / cos^2(x)). And 1 / cos^2(x) is equal to sec^2(x).
Therefore, the derivative of sec(x) is:
sec'(x) = sin(x) / cos^2(x)
= sin(x) * sec^2(x)
So, the derivative of sec(x) is sin(x) times the square of sec(x), which can also be expressed as sec(x) multiplied by tan(x):
sec'(x) = sin(x) * sec^2(x)
= sec(x) * tan(x)
I hope this explanation helps! Let me know if you have any further questions.
More Answers:
[next_post_link]