Question

find dy/dx using implicit differentiation using cosy=x for y=cos^(1)x

Answer 1

\[
\cos(y) = x \\
\text{Differentiate implicitly with respect to x:} \\
-\sin(y)y' = 1 \\
y' = -\frac{1}{\sin(y)} \\
\sin(y) = \sqrt{1-\cos^2(y)} = \sqrt{1-x^2} \\
y' = -\frac{1}{\sqrt{1-x^2}}
\]

Answer 2

The question is dy/dx(cos^(-1)x

Answer 3

\[
y = \cos^{-1}(x) \\
\frac{dy}{dx} = ? \\
\text{If }y = \cos^{-1}(x) \text{ then }\cos(y) = x \\
\text{We can find dy/dx by differentiating the latter implicitly as done above.} \\
\frac{d}{dx}\cos^{-1}(x) = -\frac{1}{\sqrt{1-x^2}}
\]

Answer 4

http://www.wolframalpha.com/input/?i=d%2Fdx+%28cos^%28-1%29%28x%29%29

Answer 5

thank you ! that makes more sense to me now!