Applying the power rule

Solved Step by Step With Explanation-Derivative of f(x)

Questions

For the following exercises, use the derivative to find f′(x).

54. f(x)=6 

59. f(x)=$\sqrt{}$2x​ 

60. f(x)= $\sqrt{}($x−6)​ 

Solved Step by Step With Explanation-Derivative of f(x)

Answer

f'(x) = -3 (The derivative of 2 is zero, and the derivative of -3x is -3.)

56. f(x) = 2x + 1

f'(x) = (2/7) * 1 * 1

f'(x) = 2/7

58. f(x) = 5x - x^2

f'(x) = 5 - 2x

= 1/(√x)

(Use the chain rule and simplify.)

61. f(x) = 9/x f'(x)

= -9/x^2

63. f(x) = 1/√x f'(x)

= (-1/2) * x^(-3/2)