Calculus III

posted by .

Derivative of Inverse Trigonometric Functions

f(x) = sin(arccos(4x))

What is f'(x)?

  • Calculus III -

    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 -

    Thanks. The next question I have is pretty similar.

    f(x) =cos(arcsin(2x))

    Find f'(x)

  • Calculus III -

    It is so similar that you should be able to do it the same way. Draw the triangle and you have sqrt(1-4x^2)
    f(x) = (1-4x^2)^.5
    f'(x) = .5 [(1-4x^2)^-.5] (-8x)
    = -4x/sqrt(1-4x^2)

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Trigonometric Functions

    Determine the Value of all six trigonometric functions of theta when given?
  2. Calculus III

    Derivative of Inverse Trigonometric Functions f(x) = cos(arcsin(2x)) What is f'(x)?
  3. Pre-Calculus-check 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 x-3 c) y=Arccos …
  4. 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.
  5. 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
  6. Trigonometry

    Write the trigonometric expression as an algebraic expression. 1.) SIN(ARCSIN X+ARCCOS X) ANSWER: 1 2.) SIN(ARCTAN 2X-ARCCOS X) ANSWER: 2x²-SquareRoot of 1-x²/Square Root of 4x²+1.
  7. Inverse Trigonometric Functions

    If sin-1(x/a) + sin-1(y/b) = sin-1(c^2/ab) then show that b^2x^2 + 2xy(a^2b^2 + c4) + a^2y^2 = c^4.
  8. 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 …
  9. pre-calculus

    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 …
  10. calculus

    for trigonometric functions and rhythmic functions questions, how do you know when to use either f(t)=A sin (w(t-a)) or f(t) = A cos ( w(t-a)) ?

More Similar Questions