## Pages

### Power rule - Worksheet

Differentiate the following expressions with the help of the power rule:

 x^2 + 2x - 1 2x + 2 3x^5 - 1/2x^4 + 6x^2 - 5 2/x^5+15 x^4+12 x 3sqrt{t} + 2cbrt{t} (3/2)t^(-1/2) + (2/3)t^(-2/3) 1/{sqrt(x)} + x^{10/3} (-1/2)x^(-3/2) + (10/3)x^(7/3) 2x^-2 + x^-1 + 3x -4x^-3 - x^-2 + 3 10/x^2 + 1/x - 1/{sqrt{x}} -20x^-3 - x^-2 + 1/2x^(-3/2) To which of the following can the power rule not be applied? a)e^x b) x c) 1^x d) x^x A and D because these contain variables as exponents. C is simplified as 1^x = 1 so it doesn't have a variable in its exponent. x^-5/{sqrt{x}} + 1/x^2 -11/2x^(-13/2) - 2x^(-3) x^n + 1/x^n nx^(n-1) - nx^(-n-1) 5x^10/{sqrt{x}} - (1/10)x^(-12) + 5/(6x^(-1/5)) + 2x^3/{cbrt{x}} 95/2x^(17/2) + 6/5x^(-13) + 1/6x^(-4/5) + 16/3x^(5/3)