Simply use the Power Rule. The derivative is 11x^7 = 11(7x^6 ) = 77x^6.
- 54 x^2 + 12
Use the Power Rule to take the derivative of each term. The derivative of 18x^3 = 18(3x^2 ) =
54 x^2 . The derivative of 12x = 12. The derivative of 11 = 0 (because the derivative of a
constant is zero). Therefore, the derivative is 54x^2 + 12.
- 6 x^11
Use the Power Rule to take the derivative of each term. The derivative of x^12 = 12x^11 . The
derivative of 17 = 0 (because the derivative of a constant is zero). Therefore, the derivative is
(12x^11 ) = 6x^11.
- −3x^8 − 2x^2
Use the Power Rule to take the derivative of each term. The derivative of x^9 = 9x^8 . The
derivative of 2x^3 = 2(3x^2 ) = 6x^2 . The derivative of 9 = 0 (because the derivative of a constant
is zero). Therefore, the derivative is − (9x^8 + 6x^2 ) = −3x^8 − 2x^2.
7. 0
Don’t be fooled by the power π^5 . is a constant so the derivative is zero.
- 64 x−9 +
Use the Power Rule to take the derivative of each term. The derivative of −8x−8 = −8(−8x−9) =
64 x−9. The derivative of (remember the shortcut that we showed you on
this page). Therefore, the derivative is 64x−9 + .
- −42x−8 −
Use the Power Rule to take the derivative of each term. The derivative of 6x−7 = 6(−7x−8) =
−42x−8. The derivative of (remember the shortcut that we showed you on
