Problem 1E: Let f(x) = 7. Using the definition of the derivative, show that f(x) = 0 for all values of x.... Problem 2E: For Exercises 121, find dydx. Assume a, b, c are constants. x2 + y3 = 8 Problem 3E: For Exercises 121, find dydx. Assume a, b, c are constants. x2 + xy y3 = xy2 Problem 4E: For Exercises 121, find dy/dx. Assume a, b, c are constants. x2 + y2 + 3x 5y= 25 Problem 5E: For Exercises 121, find dydx. Assume a, b, c are constants. xy + x + y = 5 Problem 6E: For Exercises 121, find dydx. Assume a, b, c are constants. x2y 2y + 5 = 0 Problem 7E: For Exercises 121, find dydx. Assume a, b, c are constants. x2y3 xy = 6 Problem 8E: For Exercises 121, find dydx. Assume a, b, c are constants. x=5y Problem 9E: For Exercises 121, find dydx. Assume a, b, c are constants. x+y=25 Problem 10E: For Exercises 121, find dydx. Assume a, b, c are constants. xy x 3y 4 = 0 Problem 11E: For Exercises 121, find dydx. Assume a, b, c are constants. 6x2 + 4y2 = 36 Problem 12E: For Exercises 121, find dydx. Assume a, b, c are constants. ax2 by2 = c2 Problem 13E: For Exercises 121, find dydx. Assume a, b, c are constants. ln x + ln(y2) = 3 Problem 14E: For Exercises 121, find dydx. Assume a, b, c are constants. x ln y + y3 = ln x Problem 15E: For Exercises 121, find dydx. Assume a, b, c are constants. sin(xy) = 2x + 5 Problem 16E: For Exercises 121, find dydx. Assume a, b, c are constants. ecos y = x3 arctan y Problem 17E: For Exercises 121, find dydx. Assume a, b, c are constants. arctan(x2y) = xy2 Problem 18E: For Exercises 121, find dydx. Assume a, b, c are constants. ex2+lny=0 Problem 19E: For Exercises 121, find dydx. Assume a, b, c are constants. (x a)2 + y2 = a2 Problem 20E: For Exercises 121, find dydx. Assume a, b, c are constants. x23 + y23 = a23 Problem 21E: For Exercises 121, find dydx. Assume a, b, c are constants. sin(ay) + cos(bx) = xy Problem 22E: In Exercises 2225, find the slope of the tangent to the curve at the point specified. x2 + y2 = 1 at... Problem 23E: In Exercises 2225, find the slope of the tangent to the curve at the point specified. sin(xy) = x at... Problem 24E: In Exercises 2225, find the slope of the tangent to the curve at the point specified. x3 + 2xy + y2... Problem 25E: In Exercises 2225, find the slope of the tangent to the curve at the point specified. x3 + 5x2y +... Problem 26E: For Exercises 2630, find the equations of the tangent lines to the following curves at the indicated... Problem 27E: For Exercises 2630, find the equations of the tangent lines to the following curves at the indicated... Problem 28E: For Exercises 2630, find the equations of the tangent lines to the following curves at the indicated... Problem 29E: For Exercises 2630, find the equations of the tangent lines to the following curves at the indicated... Problem 30E: For Exercises 2630, find the equations of the tangent lines to the following curves at the indicated... Problem 31E: (a) Find dydx given that x2 + y2 4x + 7y = 15. (b) Under what conditions on x and/or y is the... Problem 32E: (a) Find the slope of the tangent line to the ellipse x225+y29=1 at the point (x, y). (b) Are there... Problem 33E: (a) Find all points on y2 + xy + x2 = 1 with x = 1. (b) Find dydx for y2 + xy + x2 = 1. (c) Find the... Problem 34E: Find the equations of the tangent lines at x = 2 to the ellipse (x2)216+y24=1 Problem 35E: (a) Find the equations of the tangent lines to the circle x2 + y2 = 25 at the points where x = 4.... Problem 36E: Find the equation of the tangent line to the curve y = x2 at x = 1. Show that this line is also a... Problem 37E: If y = arcsin x then x = sin y. Use implicit differentiation on x = sin y to show that... Problem 38E: Show that the power rule for derivatives applies to rational powers of the form y = xmn by raising... Problem 39E: At pressure P atmospheres, a certain fraction f of a gas decomposes. The quantities P and f are... Problem 40E: For constants a, b, n, R, Van der Waals equation relates the pressure, P, to the volume, V, of a... Problem 41E: In Problems 4142, explain what is wrong with the statement. If y = sin(xy) then dydx = y cos(xy). Problem 42E: In Problems 4142, explain what is wrong with the statement. The formula dydx = xy gives the slope of... Problem 43E: In Problems 4344, give an example of: A formula for dydx leading to a vertical tangent at y = 2 and... Problem 44E: In Problems 4344, give an example of: A curve that has two horizontal tangents at the same x-value,... Problem 45E: True or false? Explain your answer: If y satisfies the equation y2 + xy 1 = 0, then dydx exists... format_list_bulleted