Find d r / d θ. r=tan(2-θ)

Name: Problem 25, Chapter 4: Calculus: Graphical, Numerical, Algebraic
Uploaded: 2021-08-28T07:44:07-08:00
Duration: 1 min 3 s
Channel: Adrian Co
Description: Find d r / d θ. r=tan(2-θ)

step 1 Define the derivative of this and we're going to be using chain wheel here. So we have DR d thet

Question

Find $d r / d \theta$. $$r=\tan (2-\theta)$$

   Find $d r / d \theta$.

$$r=\tan (2-\theta)$$

Calculus: Graphical, Numerical, Algebraic

Ross L. Finney,… 5th Edition

Chapter 4, Problem 25

Instant Answer

Solved by Expert Adrian Co

08/28/2021

Step 1

We want to find the derivative of $r$ with respect to $\theta$, denoted as $\frac{dr}{d\theta}$. Show more…

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Find $d r / d \theta$. $$r=\tan (2-\theta)$$

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Key Concepts

Chain Rule

The chain rule is a fundamental concept in calculus used to differentiate composite functions. When a function is composed of one function inside another, the derivative is obtained by differentiating the outer function with respect to the inner function and then multiplying by the derivative of the inner function.

Derivative of Trigonometric Functions

This concept involves knowing the standard derivatives of trigonometric functions. Specifically, for the tangent function, the derivative with respect to its argument is given by the square of the secant function, i.e., d/dx[tan(x)] = sec²(x).

Composite Functions

Working with composite functions means recognizing that a function can be expressed as the composition of two or more functions. In such cases, the chain rule is applied to effectively compute the derivative with respect to the independent variable.

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