Homework SourseProve ddxcscx csc x cotx Prove ddx cotx csc2x Find d 50 d
Prove d/dxcscx = -csc x cotx Prove d/dx cotx = -csc2x Find d 50 / dx 50[cos3x]![Prove d/dxcscx = -csc x cotx Prove d/dx cotx = -csc2x Find d 50 / dx 50[cos3x]Solution 1. (d-dx) csc(x) = (d-dx) 1/sin(x) = ( sin(x) (d-dx) (1) - 1 (d-dx) sin(](/WebImages/43/prove-ddxcscx-csc-x-cotx-prove-ddx-cotx-csc2x-find-d-50-d-1134612-1761606963-0.webp "Prove d/dxcscx = -csc x cotx Prove d/dx cotx = -csc2x Find d 50 / dx 50[cos3x]Solution 1. (d-dx) csc(x) = (d-dx) 1/sin(x) = ( sin(x) (d-dx) (1) - 1 (d-dx) sin(")
Solution
1. (d-dx) csc(x) = (d-dx) 1/sin(x) = ( sin(x) (d-dx) (1) - 1 (d-dx) sin(x) ) / sin^2(x) = -cos(x) / sin^2(x) = -csc(x)cot(x) 2. (d-dx) cot(x) = (d-dx) 1/tan(x) = ( tan(x) (d-dx) (1) - 1 (d-dx) tan(x) ) / tan^2(x) = -sec^2(x) / tan^2(x) = -csc^2(x) 3. 7.17*10^23 cos(3x)