Differentiate the following function compositions:
| Set A: | ||
| sin(4x^3-5) | 12 x^2 cos(5-4 x^3) | |
| e^sin(x) | e^(sin(x)) cos(x) | |
| log(e^x) | 1 | |
| sin(x^2-1)/cos(x^2+1) | 2 x cos(2) sec^2(x^2+1) | |
| sin^2(3x) | 3 sin(6 x) | |
| Set B: | ||
| f(x) = ln(g(x)) | f'(x) = (g'(x))/(g(x)) | |
| f(x) = e^(g(x)) | f'(x) = e^(g(x)) g'(x) | |
| f(x) = sin(g(x)) + cos(g(x)) | f'(x) = g'(x) (cos(g(x))-sin(g(x))) | |
| f(x)= 4y^3 - 5y^2 + y, where y = 3x^2 - 4 | f'(x) = 72x(3 x^2 - 4)^2 - 60x(3 x^2 - 4) + 6x | |
| f(x) = [g(x)]^n | f'(x) = n g(x)^(n-1) g'(x) | |
| Set C: | ||
| f(x) = sqrt(x^3+4x-5) | f'(x) = (3 x^2+4)/(2 sqrt(x^3+4 x-5)) | |
| f(x) = ln(x^7-x^-7) | f'(x) = (7 (x^14+1))/(x (x^14-1)) | |
| sin(x^2)+cos(2x) | 2 x cos(x^2)-2 sin(2 x) | |
| e^t^2+4t | 2 e^(t^2) t+4 | |
| (x^3+4x)^5/ln(x^2+2x) | (x^4 (x^2+4)^4 (5 (3 x^2+4) log(x (x+2))-(2 (x+1) (x^2+4))/(x+2)))/(log^2(x (x+2))) |
No comments:
Post a Comment