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HW_3_4_mod

# HW_3_4_mod - e y = x 2 e-x y(x = 6 If F x = f g x where f 3...

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Student Name: Sections 3.4 (Due: Monday, 10/01) Description : This homework will help you how to use the Chain Rule to compute derivatives. Show all work to get full credit. 1) Write the composite function in the form f ( g ( x )). y = sin 2 x u = g ( x ) = y = f ( u ) = Then find the derivative dy / dx . 2) Consider the following. (a) Write the composite function in the form f ( g ( x )) by identifying the inner function u = g ( x ) and the outer function y = f ( u ). u = g ( x ) = y = f ( u ) = (b) Find the derivative dy/dx . dy/dx = 3) Find the derivatives of the functions. y = xe -8 x y’ = g ( x ) = ( 5 + 4 x ) 3 ( 3 + x - x 2 ) 4 g’ = y’ = y = e 3 x sin x y’ = y = 8 4 - x 2 y’ =

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Student Name: y’ = y’ = y = sin(sin(sin x )) y’ = y’ = 4) Find an equation of the tangent line to the curve at the point (0, 0). y ( x ) = 5) Find an equation of the tangent line to the curve at the point (1, 1/
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Unformatted text preview: e ). y = x 2 e-x y (x) = 6) If F ( x ) = f ( g ( x )), where f ( 3 ) = 6 , f '( 3 ) = 1 , f '( 1 ) = 1 , g ( 1 ) = 3 , and g '( 1 ) = 5 , find F '( 1 ). 7) If h ( x ) is given below, where f ( 5 ) = 7 and f '( 5 ) = 2 , find h '( 5 ). 8) For what values of r does the function y = e rx satisfy the equation y '' + 7 y ' - 18 y = 0? r = (smaller value) r = (larger value) 9) Find the 30th derivative of y = cos 3 x . 10) The displacement of a particle on a vibrating string is given by the equation below, where s is measured in centimeters and t in seconds. Find the velocity of the particle after t seconds. v ( t ) = cm/s...
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