HW_3_5_mod

# HW_3_5_mod - and use implicit differentiation to find dx dy...

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Student Name: Sections 3.5 (Due: Thursday, 10/04) Description : This homework will help you understand the concepts of implicit functions and implicit curves. You need to know the method of implicit differentiation and the inverse trigonometric functions. Show all work to get full credit. 1 ) Find y ' by implicit differentiation. y ' = 2 ) Find y ' by implicit differentiation.: cos x + √ y = 1 y ' = 3 ) Find dy / dx by implicit differentiation: x 3 ( x + y ) = y 2 ( 5 x - y ) dy / dx = 4 ) Find dy / dx by implicit differentiation: x 2 y 2 + x sin y = 4 dy / dx = 5 ) Find dy/dx by implicit differentiation: dy/dx = 6 ) Find dy / dx by implicit differentiation: 7 cos x sin y = 2 dy / dx = 7 ) Find dy / dx by implicit differentiation: e x / y = 5 x - y dy / dx = 8 ) Find dy/dx by implicit differentiation: dy/dx = 9 ) If f ( x ) + x 2 [ f ( x )] 5 = 246 and f (1) = 3 , find f '(1). f '(1) = 10 ) Regard y as the independent variable and x as the dependent variable

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Unformatted text preview: and use implicit differentiation to find dx / dy . Remember that sin 2 x means (sin( x )) 2 . y sec x = x tan y dx / dy = Student Name: 11 ) Find an equation of the tangent line to the curve at the given point y = 12 ) Find an equation of the tangent line to the curve x 2/3 + y 2/3 = 4 at the given point y = 13 ) Find the points on the lemniscate, given below, where the tangent is horizontal. 14 ) Find the derivative of the function. Simplify if possible. y ' = 15 ) Find the derivative of the function. Simplify if possible. y = sin-1 ( 4 x + 2 ) y ' = 16 ) Find the equations of both the tangent lines to the ellipse x 2 + 4 y 2 = 36 that pass through the point (12,3). y = (horizontal tangent line) y = (non-horizontal tangent line)...
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HW_3_5_mod - and use implicit differentiation to find dx dy...

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