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Chapter 2: Q 39 (page 238)

If $A = π r^{2}$ ,find $\frac{d A}{d r} .$

Short Answer

Expert verified

$\frac{d A}{d r} = 2 πr$

Step by step solution

01

Step 1:Gievn information

The given expression is $A = π r^{2}$

02

Step 2:Simplification

$A = π r^{2}$

Differentiating w.r.t x

width="124" height="41" role="math">⇒dAdr=ddrπr2

$\Rightarrow \frac{d A}{d r} = 2 πr$

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Most popular questions from this chapter

Sketch a graph of the associated slope function f' for each function f.

Find the derivatives of the functions in Exercises 21–46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.

$f (x) = {(x^{\frac{1}{3}} - 2 x)}^{- 1}$

In Exercises 69–80, determine whether or not $f$ is continuous and/or differentiable at the given value of $x$ . If not, determine any left or right continuity or differentiability. For the last four functions, use graphs instead of the definition of the derivative.

$f (x) = \{\begin{cases} x^{2}, i f x \leq 1 \\ 2 x - 1, i f x > 1, \end{cases} x = 1$

State the chain rule for differentiating a composition $g (h (x))$ of two functions expressed

(a) in “prime” notation and

(b) in Leibniz notation.

Use the definition of the derivative to find $f'$ for each function $f$ in Exercises

$f (x) = \frac{3}{\sqrt{x}}$

See all solutions

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