Back{Use of Tech} Angle of elevation A small plane, moving at 70 m/s, flies horizontally on a line 400 meters directly above an observer. Let θ be the angle of elevation of the plane (see figure). <IMAGE>
a. What is the rate of change of the angle of elevation dθ/dx when the plane is x=500 m past the observer?
{Use of Tech} Angle of elevation A small plane, moving at 70 m/s, flies horizontally on a line 400 meters directly above an observer. Let θ be the angle of elevation of the plane (see figure). <IMAGE>
b. Graph dθ/dx as a function of x and determine the point at which θ changes most rapidly.
9–61. Evaluate and simplify y'.
y = tan^−1 √t²−1
9–61. Evaluate and simplify y'.
y = x²+2x tan^−1(cot x)
9–61. Evaluate and simplify y'.
y = 2x² cos^−1 x+ sin^−1 x
Evaluate d/dx(x sec^−1 x) |x = 2 /√3.
Consider the following functions. In each case, without finding the inverse, evaluate the derivative of the inverse at the given point.
y =√x³+x−1 at y=3
Find the derivative of the inverse of the following functions. Express the result with x as the independent variable.
f(x) = x^-1/3