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Consider the following. cos(x) + y = 4 (a) Find y' by implicit differentiation. y' =...
6x2 − y2 = 9 (a) Find y' by implicit differentiation. y' = (b) Solve the equation explicitly for y and differentiate to get y' in terms of x. y' = ±
Consider the curve de fired by the equation xt a) using expression implicit in x differentiation, solve and y for dy as an b) the in Find the equation of the corce at the point c2,1). the form y=mxth tangent line to to Put the equation.
⒈ Consider the equation x2y2=c, where c is a real constant.(a) Assuming that this implicitly defines a differentiable function y=f(x), use implicit differentiation to find an expression for dy/dx.(b) For what combination of x and c is your answer to Part (a) valid?(c) Assuming c>0, find all of the possible functions f and verify that the derivative f' satisfies the expression found in Part (a).
dy Find by implicit differentiation for the following equation. x"y = 8x+6y +9
17 EMTH210-1851 (b) Consider the following functions: F = x-y-e, (0) Use implicit differentiation to find
4. Consider the following initial value problem: y(0) = e. (a) Solve the IVP using the integrating factor method. (b) What is the largest interval on which its solution is guaranteed to uniquely exist? (c) The equation is also separable. Solve it again as a separable equation. Find the particular solution of this IVP. Does your answer agree with that of part (a)? 5 Find the general solution of the differential equation. Do not solve explicitly for y. 6,/Solve explicitly...
11. (5 points each) Find the derivative of each function. DO NOT simplify your answers. cos(x) a) f(x) = 1-tan(x) b) f(x) – tan-" (4x²) dy 12. Consider the equation x² + xy + y² = 1. Find an expression for by implicit differentiation. dx
What is the implicit derivative of the following equation?
y= (4 + cos²(x))
Find dy/dx by implicit differentiation. x?y? - y = x dy/dx =
Determine whether the equation is exact. If it is, then solve it. (cos x cos y - 10x)dx - (sin x sin y + 2y)dy = 0 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. = C, where is an arbitrary constant. O A. The equation is exact and an implicit solution in the form F(x,y) = C is (Type an expression using x and y as the variables.) OB. The...