Sunday

March 29, 2015

March 29, 2015

Posted by **Sean** on Tuesday, January 22, 2008 at 4:26pm.

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

What is f'(x)?

- Calculus III -
**drwls**, Tuesday, January 22, 2008 at 4:47pmf(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**, Tuesday, January 22, 2008 at 8:38pmThanks. The next question I have is pretty similar.

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

Find f'(x)

- Calculus III -
**Damon**, Tuesday, January 22, 2008 at 9:17pmIt 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)

**Answer this Question**

**Related Questions**

Calculus (Derivatives of Inverse Functions) - Suppose f(x) = sin(pi cos(x)). On ...

Calculus III - Derivative of Inverse Trigonometric Functions f(x) = cos(arcsin(...

TRIGONOMETRY - Write the following trigonometric expression as an algebraic ...

Trigonometry - Write the trigonometric expression as an algebraic expression. 1...

Trigonometric Functions - Determine the Value of all six trigonometric functions...

Pre-Calculus-check answers - State the period and phase shift of the function y...

Trigonometry - Use inverse trigonometric functions to find the solutions of the ...

Trigonometry - Use inverse trigonometric functions to find the solutions of the ...

Trigonometry - Use inverse trigonometric functions to find the solutions of the ...

Trigonometry - IM STUCK ON THESE :( 1. What is the equation for shifting the ...