Find dy/dx cos(2y)=x

Problem

cos(2*y)=x

Solution

1. Differentiate both sides with respect to x using the chain rule for the term involving y

d(cos(2*y))/d(x)=d(x)/d(x)

2. Apply the chain rule to the left side, noting that the derivative of cos(u) is −sin(u) and the derivative of 2*y is 2d(y)/d(x)

−2*sin(2*y)d(y)/d(x)=1

3. Isolate the derivative by dividing both sides of the equation by −2*sin(2*y)

d(y)/d(x)=1/(−2*sin(2*y))

4. Simplify the expression to its final form.

d(y)/d(x)=−1/(2*sin(2*y))

Final Answer

d(y)/d(x)=−1/(2*sin(2*y))

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