Use the following table to find the given derivatives. x 1 2 3 4 f(x)

step 1 Let's find the derivative of f of x over g of x evaluated at x equals two. Now we have a table,

Use the following table to find the given derivatives. ...

Use the following table to find the given derivatives. $$\begin{array}{lclclclc} x & 1 & 2 & 3 & 4 \\ \hline f(x) & 5 & 4 & 3 & 2 \\ f^{\prime}(x) & 3 & 5 & 2 & 1 \\ g(x) & 4 & 2 & 5 & 3 \\ g^{\prime}(x) & 2 & 4 & 3 & 1 \end{array}$$ $$\left.\frac{d}{d x}\left(\frac{f(x)}{g(x)}\right)\right|_{x=2}$$

Use the following table to find the given derivatives.
$$\begin{array}{lclclclc}
x & 1 & 2 & 3 & 4 \\
\hline f(x) & 5 & 4 & 3 & 2 \\
f^{\prime}(x) & 3 & 5 & 2 & 1 \\
g(x) & 4 & 2 & 5 & 3 \\
g^{\prime}(x) & 2 & 4 & 3 & 1
\end{array}$$
$$\left.\frac{d}{d x}\left(\frac{f(x)}{g(x)}\right)\right|_{x=2}$$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Quotient Rule

The quotient rule is a differentiating technique used when a function is expressed as the ratio of two differentiable functions. It states that, for a function h(x) = f(x)/g(x), the derivative h'(x) is computed as (f'(x)g(x) - f(x)g'(x)) divided by [g(x)]². This rule is essential when directly applying differentiation to quotients without simplifying first.

Derivative

A derivative measures the instantaneous rate of change of a function with respect to a variable. It represents how a function's output changes as the input changes, and it is a central concept in calculus. The derivative can be computed by applying various differentiation rules, such as the quotient rule for ratios of two functions.

Using Tabular Data for Evaluation

When values of functions and their derivatives are provided in a table, these can be substituted directly into differentiation formulas to evaluate derivatives at specific points. This approach is particularly useful when a functional expression is not available or when working directly with discrete data points.

Transcript

Please give Ace some feedback