this page). Therefore, the derivative is −42x−8 − .
10.
Use the Power Rule to take the derivative of each term. The derivative of x−5 = −5x−6. To find
the derivative of , we first rewrite it as x−8. The derivative of x−8 = −8x−9. Therefore, the
derivative is −5x−6 − 8x−9 = .
- 216 x^2 − 48x + 36
First, expand (6x^2 + 3)(12x − 4) to get 72x^3 − 24x^2 + 36x − 12. Now, use the Power Rule to
take the derivative of each term. The derivative of 72x^3 = 72(3x^2 ) = 216x^2 . The derivative of
24 x^2 = 24(2x) = 48x. The derivative of 36x = 36. The derivative of 12 = 0 (because the
derivative of a constant is zero). Therefore, the derivative is 216x^2 − 48x + 36.
- −6 − 36x^2 + 12x^3 − 5x^4 − 14x^6
First, expand (3 − x − 2x^3 )(6 + x^4 ) to get 18 − 6x − 12x^3 + 3x^4 − x^5 − 2x^7 . Now, use the Power
Rule to take the derivative of each term. The derivative of 18 = 0 (because the derivative of a
constant is zero). The derivative of 6x = 6. The derivative of 12x^3 = 12(3x^2 ) = 36x^2 . The
derivative of 34x^4 = 3(4x^3 ) = 12x^3 . The derivative of x^5 = 5x^4 . The derivative of 2x^7 = 2(7x^6 ) =
14 x^6 . Therefore, the derivative is −6 − 36x^2 + 12x^3 − 5x^4 − 14x^6.
Don’t be fooled by the powers. Each term is a constant so the derivative is zero.
14.
First, expand to get = . Next,
rewrite the terms as: 4x−4 − 2x−5 − 6x−6. Now, use the Power Rule to take the derivative of
each term. The derivative of 4x−4 = 4(−4x−15) = −16x−5. The derivative of 2x−5 = 2(−5x−6) =
−10x−6. The derivative of 6x−6 = −36x−7. Therefore, the derivative is −16x−5 + 10x−6 + 36x−7 =
.
