3.5 Homework - Implicit Differentiation (Homework)

6. [-/1 Points] DETAILS SCALCET8 3.5.508.XP. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find dy/dx by implicit differentiation. 6 cos(x) sin(y) = 3 y' Need Help? Watch It7. [-/1 Points] DETAILS SCALCET8 3.5.503.XP.MI.SA. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise Find dy/dx by implicit differentiation. x7 + y4 = 4 Step 1 When finding -= y' by implicit differentiation, we consider y to be a function of x. This means that whenever a derivative is calculated for an expression that includes the variable y, the Chain Rule requires that we multiply the derivative by y'. For example, - 1 2 = ( 24 ) (x). Similarly, Submit Skip (you cannot come back)8. [-/1 Points] DETAILS SCALCET8 3.5.066. MY NOTES ASK YOUR TEACHER Two curves are orthogonal if their tangent lines are perpendicular at each point of intersection. Are the given families of curves orthogonal trajectories of each other? That is, is every curve in one family orthogonal to every curve in the other family? x2 + 12 = ax x2 + 12 = by O Yes, every curve in the first family of curves is orthogonal to every curve in the second family of curves. O No, there are curves in the first family of curves that are not orthogonal to every curve in the second family of curves. Sketch both families of curves on the same axes. -10 O O - 10 -10 O O9. [-/1 Points] DETAILS SCALCET8 3.5.JIT.010. MY NOTES ASK YOUR TEACHER Rewrite the expression as an algebraic expression in x. cos(sin (x)) Need Help? Watch It 10. [-/1 Points] DETAILS SCALCET8 3.5.JIT.001.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER The given equation is either linear or equivalent to a linear equation. Solve the equation. (If there is no solution, enter NO SOLUTION. If all real numbers are solutions, enter REALS.) 5x + 7 = 52 X = Need Help? Watch It Master It