Respuesta :
Using the power rule, the derivatives are given as follows:
a) [tex]f^{\prime}(2) = -\frac{1}{4}[/tex].
b) [tex]f^{\prime}(3) = 30[/tex].
What is the power rule for a derivative?
Suppose we have a power function given by:
[tex]f(x) = x^n[/tex]
The derivative of the function is given by:
[tex]f^{\prime}(x) = n \times x^{n-1}[/tex]
Item a:
The function is:
[tex]f(x) = \frac{1}{x} = x^{-1}[/tex]
Then the derivative is:
[tex]f^{\prime}(x) = -x^{-2} = -\frac{1}{x^2}[/tex]
When x = 2, the derivative is:
[tex]f^{\prime}(2) = -\frac{1}{4}[/tex]
Item b:
The function is:
[tex]f(x) = 5x^2[/tex]
Then the derivative is:
[tex]f^{\prime}(x) = 10x[/tex]
When x = 3, the derivative is:
[tex]f^{\prime}(3) = 30[/tex]
More can be learned about derivatives at https://brainly.com/question/2256078
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