Answers submitted 8csc4xcot4x correct correct answers

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Answer(s) submitted: -8csc(4x)cot(4x) (correct) Correct Answers: -2*4/[tan(4*x)*sin(4*x)] 8. (1 point) Let f ( x ) = ( 3 x 2 - 6 ) 5 ( 2 x 2 - 4 ) 15 f 0 ( x ) = Answer(s) submitted: 30x(3xˆ2 - 6)ˆ4 * (2xˆ2-4)ˆ15 + (3xˆ2 - 6)ˆ5 * 60x (2xˆ2-4)ˆ14 (correct) Correct Answers: (3*xˆ2+-6)ˆ4 * (2*xˆ2+-4)ˆ14 * (240*xˆ3 + -480*x) 9. (1 point) Let f ( x ) = 4cos ( sin x ) f 0 ( x ) = Solution: SOLUTION By the chain rule: f 0 ( x ) = - 4sin ( sin x ) d dx ( sin x ) = - 4sin ( sin x )) · cos x Answer(s) submitted: -4sin(sin(x))cos(x) (correct) Correct Answers: -4*sin(sin(x))*cos(x) 10. (1 point) If f ( t ) = 6 t - 3 t 4 7 , find f 0 ( t ) . Solution: SOLUTION f 0 ( t ) = 4 7 6 t - 3 t - 3 7 d dt 6 t - 3 t = 4 7 6 t - 3 t - 3 7 6 + 3 t 2 Answer(s) submitted: 4 (6tˆ2+3) / (( 7tˆ(11/7) ( 6tˆ2-3 )ˆ(3/7) )) (correct) Correct Answers: 4/7*(6*t-3/t)**(4/7-1)*(6+3/(t**2)) 11. (1 point) Let f ( x ) = - 7 x 3 - 9 x f 0 ( x ) = Solution: SOLUTION We first rewrite the function as f ( x ) = - 7 x ( 3 - 9 x ) - 1 / 2 We then have f 0 ( x ) = ( 3 - 9 x ) - 1 / 2 d dx ( - 7 x ) - 7 x d dx ( 3 - 9 x ) - 1 / 2 by the product ru = - 7 ( 3 - 9 x ) - 1 / 2 + 7 2 x ( 3 - 9 x ) - 3 / 2 d dx ( 3 - 9 x ) by the chain ru = - 7 ( 3 - 9 x ) - 1 / 2 - 63 2 x ( 3 - 9 x ) - 3 / 2 Answer(s) submitted: - 7 (2-3x) / ( 2(-3x+1)sqrt(-9x+3) ) (correct) Correct Answers: (-7*(3-9*x)+-7*9*x/2)/(3-9*x)**(3/2) 12. (1 point) Let y = ( 7 + cos 2 x ) 9 dy dx = Solution: SOLUTION Applying the chain rule twice, gives: dy dx = 9 ( 7 + cos 2 x ) 8 · d dx ( 7 + cos 2 x ) by the chain rule = 9 ( 7 + cos 2 x ) 8 · 2 · cos x · d dx ( cos x ) by the chain rule = 9 ( 7 + cos 2 x ) 8 · 2 · cos x · ( - sin x ) = - 18cos x sin x ( 7 + cos 2 x ) 8 Answer(s) submitted: 2
-18(7+cosˆ2(x))ˆ8*cos(x)sin(x) (correct) Correct Answers: -2*cos(x)*sin(x)*9*(7+(cos(x))ˆ2)ˆ(9-1) 13. (1 point) Find an equation of the tangent line to the curve y = sin ( 3 x )+ cos ( 4 x ) at the point ( π 6 , y ( π 6 )) . Tangent line: y = Solution: SOLUTION The derivative of the function is dy dx = 3cos ( 3 x ) - 4sin ( 4 x ) The slope of the tangent line at the point ( π 6 , y ( π 6 )) is dy dx x = π / 6 = 3cos ( 1 2 π ) - 4sin ( 2 3 π ) = - 2 3

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