Why do I keep getting stuck when taking the derivative of the inverse cosecant function?
Hello all,
So I’m attempting to directly prove that the derivative of the inverse cosecant: (d/dx) csc^-1(x) = -1 / [abs(x) sqrt(x^2 – 1)]
To get started, I swap x and y in the cosecant function expression y = csc^-1(x), and get:
x = csc(y)
Then I go ahead and take the derivative of that expression, and I get:
1 = -csc(y)cot(y) y’
So,
y’ = – 1 / [csc(y)cot(y)]
How do I change csc(y)cot(y) to the required abs(x) sqrt(x^2 -1)? Is this some bizarre trigonometric/Pythagorean identity of which I am not aware?
Topic:
calculus
Observing members:
0
Composing members: 0
Composing members: 0
Answers
virtualist
(2442
)“Great Answer”
(2)
)“Great Answer”
(2)
Beta_Orionis
(3410)“Great Answer”
(2)
)“Great Answer”
(2)
ItalianPrincess1217
(11979)“Great Answer”
(1)
)“Great Answer”
(1)
faye
(17857)“Great Answer”
(0)
)“Great Answer”
(0)
Psychedelic_Zebra
(5090)“Great Answer”
(1)
)“Great Answer”
(1)
HeroicZach
(195)“Great Answer”
(1)
)“Great Answer”
(1)
ccrow
(8097)“Great Answer”
(1)
)“Great Answer”
(1)
