Question

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

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

Calculus

James Stewart 7th Edition

Chapter 2, Problem 32

Instant Answer

Solved by Expert Amelia Hardy

09/11/2022

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Step 1: We need to find the derivative of $f(x) = \frac{4}{\sqrt{1-x}}$. Show more…

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

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Key Concepts

Derivative Evaluation at a Point

Evaluating the derivative at a specific point involves computing the general derivative of the function and then substituting the given point into this derivative. This process yields the slope of the tangent line to the function at that particular point.

Chain Rule

The chain rule is a method for differentiating composite functions. It states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function multiplied by the derivative of the inner function. This rule is essential when dealing with functions that are nested within each other.

Power Rule

The power rule is a fundamental differentiation technique used to differentiate functions of the form x^n, where n is any real number. When a function is expressed in exponent form, the derivative is obtained by multiplying by the exponent and reducing the exponent by one.

Derivative

The derivative represents the instantaneous rate of change of a function with respect to its variable. It is defined as the limit of the difference quotient as the increment approaches zero and provides a measure of how a function’s output changes with a small change in input.

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