Calculus III
posted by Sean .
Derivative of Inverse Trigonometric Functions
f(x) = sin(arccos(4x))
What is f'(x)?

Calculus III 
drwls
f(x)= sin(arccos(4x)) = sqrt(1  16x^2)
(To prove that, draw yourself a triangle with cos A = 4x and figure out the sin of A)
let u = 1  16x^2
f(u) = sqrt u
f'(x) = df/dx = df/du du/dx
= (1/2)(u)^1/2 * 32 x
= 16 x/sqrt[1  16x^2] 
Calculus III 
Sean
Thanks. The next question I have is pretty similar.
f(x) =cos(arcsin(2x))
Find f'(x) 
Calculus III 
Damon
It is so similar that you should be able to do it the same way. Draw the triangle and you have sqrt(14x^2)
f(x) = (14x^2)^.5
f'(x) = .5 [(14x^2)^.5] (8x)
= 4x/sqrt(14x^2)
Respond to this Question
Similar Questions

Trigonometric Functions
Determine the Value of all six trigonometric functions of theta when given? 
Calculus III
Derivative of Inverse Trigonometric Functions f(x) = cos(arcsin(2x)) What is f'(x)? 
PreCalculuscheck answers
State the period and phase shift of the function y=4tan(1/2x + 3pi/8) a) 2pi, 3pi/4 b) pi, 3pi/8 c) 2pi, 3pi/8 d) pi, 3pi/8 Answer: d 2) What is the equation for the inverse of y=cos x+3: a) y=Arccos(x+3) b) y=Arccos x3 c) y=Arccos … 
Calculus (Derivatives of Inverse Functions)
Suppose f(x) = sin(pi cos(x)). On any interval where the inverse function y = f^1(x) exists, the derivative of f^1(x) with respect to x is: I've come as far as y = arccos ((arcsin(x))/pi), but I am not certain this is right. 
TRIGONOMETRY
Write the following trigonometric expression as an algebraic expression in x free of trigonometric or inverse trigonometric functions sin(cos^1 x) 1≤x≤1 
Trigonometry
Write the trigonometric expression as an algebraic expression. 1.) SIN(ARCSIN X+ARCCOS X) ANSWER: 1 2.) SIN(ARCTAN 2XARCCOS X) ANSWER: 2x²SquareRoot of 1x²/Square Root of 4x²+1. 
Inverse Trigonometric Functions
If sin1(x/a) + sin1(y/b) = sin1(c^2/ab) then show that b^2x^2 + 2xy(a^2b^2 + c4) + a^2y^2 = c^4. 
Math
y=arccos(sin(x)), find dy/dx and sketch it's graph(I guess I can do this on wolframalpha after I'm done solving the question). And by arcsin I mean inverse of the expression(written like cos^1(sin(x)), but is not 1/cos(sinx) but the … 
precalculus
Rewrite the following expression as an algebraic function of x sin(arccos(x/2)) I know sine is y, which is opposite over hypotenuse. I also know that arccos is the inverse of cosine. I'm confused on what the question is asking and … 
calculus
for trigonometric functions and rhythmic functions questions, how do you know when to use either f(t)=A sin (w(ta)) or f(t) = A cos ( w(ta)) ?