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# quiz3 - Quiz 1 If f(x = x2 ex nd f(x sin(x 2 If g(x = nd...

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Quiz 1. If f ( x ) = x 2 e x , find f 0 ( x ). 2. If g ( x ) = sin( x ) 1 + cos( x ) , find g 0 ( x ). 3. If h ( x ) = x 7 + 3 x 6 - 5 x 3 + 2 x 2 - x + 1, find h 0 ( x ) and h 00 ( x ). 4. Find the equation of the tangent line to the curve y = (1 - 2 x ) 100 at the point (0 , 1).

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Solutions 1. f 0 ( x ) = d dx ( x 2 )e x + x 2 d dx e x = 2 x e x + x 2 e x = x e x (2 + x ). 2. If g(x)=sin(x) / (1+cos(x)), find g 0 ( x ) = (1 + cos( x )) d dx (sin( x )) - sin( x ) d dx (1 + cos( x )) (1 + cos( x )) 2 = (1 + cos( x )) cos( x ) - sin( x )( - sin( x )) (1 + cos( x )) 2 = cos( x ) + cos 2 ( x ) + sin 2 ( x ) (1 + cos( x )) 2 = cos( x ) + 1 (1 + cos( x )) 2 = 1 1 + cos( x ) . 3. h 0 ( x ) = 7 x 6 + 18 x 5 - 15 x 2 + 4 x -
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