Find dy/dx x^4=cot(y)

Problem

x4=cot(y)

Solution

1. Differentiate both sides with respect to x using implicit differentiation.

2. Apply the power rule to the left side of the equation.

d(x4)/d(x)=4*x3

3. Apply the chain rule to the right side of the equation, noting that the derivative of cot(y) is −csc2(y)

d(cot(y))/d(x)=−csc2(y)d(y)/d(x)

4. Equate the derivatives from both sides to form a new equation.

4*x3=−csc2(y)d(y)/d(x)

5. Isolate the derivative d(y)/d(x) by dividing both sides by −csc2(y)

d(y)/d(x)=(4*x3)/(−csc2(y))

6. Simplify the expression using the trigonometric identity 1/csc(y)=sin(y)

d(y)/d(x)=−4*x3*sin2(y)

Final Answer

d(y)/d(x)=−4*x3*sin2(y)

Want more problems? Check here!