Exam 3: Topics in Deifferentiation

Find .

If x² - y² = 77, find dy/dx.

Let y = 2x² and dx = 0.04 at x = 4. Find dy.

Find if .

A baseball diamond is a square 90 feet on each side. A player is running from home to first base at the rate of 20 feet per second. At what rate is his distance from second base changing when he is 35 feet from first base? (Round your answer to three decimal places.)

Evaluate. .

If y = (ln 6x)e^3x , find .

Find if .

If , find by logarithmic differentiation.

If y = x⁴, find the formula for $\Delta$ y.

Find the formula for dy if .

Find the formula for $\Delta$ y if y = csc x.

Let . Find dy if dx = 2 and the initial value of x is x = 2.

f(x) = 6^x . Find .

y = 2 ln 4x. Find .

Find if

Use a differential to approximate .

Two ships leave port at noon. One ship sails north at 12 miles per hour and the other sails east at 9 miles per hour. At what rate are the two ships separating 2 hours later?

Find if

A point P is moving along a curve whose equation is . When P = (6, 10) , y is increasing at a rate of 3 units/s. How fast is x changing?