How to find dy/dx if y = cos^−1(e^4x).

Answer 1

Recall that the derivative of cos^-1(x) is -1/√(1-x²), so by using the chain rule:

d/dx cos^-1(e^4x) = (e^4x)' • -1/√(1-(e^4x)²) = 4e^4x • -1/√(1-e^8x) = -4e^4x/√(1-e^8x)

Hope this helped!

Answer 2

Hello Emily,

cos^-1(e^4x) is the same thing as arccos(e^4x), and by definition:

(arccos u(x))' = -u'/√(1-u²) ---- you can find it in a table for derivatives of inverse trigonometric functions.

Here: u(x) = e^4x so u' = 4e^4x

Therefore: [arccos(e^4x)]' = -4e^4x/ √(1-(e^4x)²) = -4e^4x/ √(1-e^8x)

Answer: if dy/dx if y = cos^−1(e^4x), then dy/dx = -4e^4x/ √(1-e^8x)