2) If f(x) = x^{n}, then f '(x) = nx^{n - 1}.
b) f(x) = x^{5}, f '(x) = 5x^{4}.
c) f(x) = x^{-4}, f '(x) = -4x^{-5}.
d) f(x) = x^{1/2}, f '(x) = 1/2(x)^{-1/2}.
Easy to do. Bring the power out front and decrease the power by one!
b) f(x) = -4x^{3}, f '(x) = -12x^{2}.
b) f(x) = x^{3} + 4x^{2} - 5x + 3, f '(x) = 3x^{2} + 8x - 5.
2) f(x) = 5x^{3} - 4x^{2} + 3x -7
3) f(x) = 1/x^{2}
4) f(x) =
5) f(x) =
2) f '(x) = 15x^{2} - 8x + 3, f '(2) = 15(2)^{2} - 8(2) + 3 = 15(4) - 16 + 3 = 47
3) f(x) = x^{-2}, f '(x) = -2x^{-3}, f '(2) = -2(2)^{-3} = -2/8
4)
5) f '(x) = 4x^{2} + 3/x^{2} - 8/x^{3} , f '(2) = 4(2)^{2} + 3/(2)^{2} - 8/(2)^{3} = 15 3/4