Calculus Implicit Differentiation and Trig (3.7 - 3.10 Briggs) Flashcards

1

If y = tan^-1(x), then y' =

2

True or False: If y is a function of x, then d/dx(x + y) = 1 + y'

3

True or False: d/dx( cot(5x) ) = -csc²(5x)

4

Double points! Find y' using implicit differentiation: xy = y² + 1

5

The function f(x)^g(x) is equivalent to e raised to what power?

6

If f(x) = 3arcsin(x), then f'(x) =

7

Find the slope of the line tangent to f\left(x\right)=\sqrt{x+8} at x = 1.

8

Suppose p(k) represents the pressure on a submarine at depth k, and k changes as a function of time (t). Then, dp/dt =

9

Last question: How can one prove that d/dx( ln x ) = 1/x ?

10

Find the slope of the ellipse 4x² + y² = 5 at the point (1, 1).

11

Find dh/dt given h(t) = ln(t) + 1 + e^sint

Calculus Implicit Differentiation and Trig (3.7 - 3.10 Briggs)