Question

What’s the derivative of the function: A) f(x)= 1/x , in point 2. B) f(x)= 5x^2 , in point 3

Answer 1

Using the power rule, the derivatives are given as follows:

a) $f^{\prime}(2) = -\frac{1}{4}$.

b) $f^{\prime}(3) = 30$.

What is the power rule for a derivative?

Suppose we have a power function given by:

$f(x) = x^n$

The derivative of the function is given by:

$f^{\prime}(x) = n \times x^{n-1}$

Item a:

The function is:

$f(x) = \frac{1}{x} = x^{-1}$

Then the derivative is:

$f^{\prime}(x) = -x^{-2} = -\frac{1}{x^2}$

When x = 2, the derivative is:

$f^{\prime}(2) = -\frac{1}{4}$

Item b:

The function is:

$f(x) = 5x^2$

Then the derivative is:

$f^{\prime}(x) = 10x$

When x = 3, the derivative is:

$f^{\prime}(3) = 30$

More can be learned about derivatives at brainly.com/question/2256078

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