cos(x+y)=pi+x^2y

Question

Find dy/dx for the function:

Answer 1

cos(x + y) = πx²y

 

We will use implicit differentiation by taking the derivative of both sides of equation using the chain rule.

 

[cos(x + y)]' = [πx²y]'

 

(1 + y')[-sin(x+y)] = 2πxy + πx²y'

 

-sin(x + y) - y'sin(x + y) = 2πxy + πx²y'

 

 

Now we bring all the terms with y' on one side of the equation.

 

-y'sin(x + y) - πx²y' = sin(x + y) + 2πxy

 

y' [-sin(x + y) - πx²] = sin(x + y) + 2πxy

 

 

Finally divide by -sin(x + y) - πx² both sides of equation.