# The derivative of f ′ ( t ) = d θ d t where θ = π 6 .

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 4, Problem 35RE
To determine

## To find:The derivative of f′(t)=dθdt where θ=π6 .

Expert Solution

The angle of elevation of the sun increasing at 400ft/h

### Explanation of Solution

Given:

400ft tall building and dθdt=0.25rad/h (negative because decreasing ) Concept used:

The left derivative and right derivative of a function f at a point x=c are , equal

f'(c)=limh0f(ch)f(c)hf+'(c)=limh0+f(c+h)f(c)h

Calculation:

An equation related to the quantities

x400=cotθx=400cotθ..............(1)

Differentiating equation (1) wih respect to t

dxdt=400csc2θdθdt

Values for the moment in time

dxdt=400csc2π6(0.25)dxdt=400ft/h

The angle of elevation of the sun increasing at 400ft/h .

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