Aug 3, 2014 · dy/dx = -1/sqrt(x^4 - x^2) Process: 1.) y = "arccsc"(x) First we will rewrite the equation in a form that is easier to work with. Take the cosecant of both sides: 2.) csc y = x Rewrite in terms of sine: 3.) 1/siny = x Solve for y: 4.) 1 = xsin y 5.) 1/x = sin y 6.) y = arcsin (1/x) Now, taking the derivative should be easier. It's now just a matter of chain rule. We know that d/dx[arcsin alpha ...

The basic inverse trigonometric functions are used to find the missing angles in right triangles. While the regular trigonometric functions are used to determine the missing sides of right angled triangles, using the following formulae:

Jun 30, 2016 · - 2/(x sqrt(x^2 - 4)) if y = csc^{-1} (x/2) then csc y = x/2 [..... Which means that color{red}{sin y = 2/x}] so D_x(csc y = x/2) \\implies - csc y \\ cot y \\ y ' = 1/2 [D_z (csc z) = - csc z cot z is a well known derivative] So we have y ' = 1/2 1/(- csc y \\ cot y) = - 1/2 sin y \\ tan y the significance of the text in red is this: because it should be clear that tan y = 2/sqrt(x^2 - 4) so ...

Mar 9, 2015 · Method: To integrate #arc sec (x)#, substitution, then integrate by parts.. You'll also need #int secu du#, which can be done by substitution and partial fractions.

The derivatives of inverse trigonometric functions can be computed by using implicit differentiation followed by substitution.

Oct 21, 2015 · #arcsin(x) = sin^-1(x)# is the inverse function of the function #sin(x)# That is: If #x in (-pi/2, pi/2)#, then #arcsin(sin(x)) = x#

Feb 26, 2016 · 36^@87 tan X = 3/5 --> cot X = 5/3 arccsc (5/3) = arcsin (3/5) Calculator --> sin y = 3/5 --> arc y = 36^@87

Nov 23, 2016 · sin(arcsec(x))=sqrt(x^2-1)/x arcsecx means the angle whose secant ratio is x i.e. if arcsec(x)=theta, we have sectheta=x.

Nov 15, 2017 · Original syntax: How do you differentiate #y= arctan sqrt(x^2 -1) + arccsc x#?. Calculus Differentiating Trigonometric Functions Differentiating Inverse Trigonometric Functions

Jul 17, 2018 · See graph and my idiosyncratic explanation. y = arcsec x = arc cos(1/x) , Conventionally limited ( for trigonometric arccos ) y in [ 0, pi ].