Calculus Test Review - Chapter 2B

Trig Functions

100

Derivative of f(x) = 4sin3x - x

12cos3x - 1

200

Derivative of f(x) = 2sin2xcos2x

4cos²2x - 4sin²2x

300

Equation of tangent line to f(x) = x²cosx at x = pi/2

y = - (pi²/4)(x-pi/2)

400

The velocity of a mass on a spring at time t = pi whose position is given by s(t) = (cos t)/t

1/(pi²)

500

Derive the rule (d/dx)(cot x) = -csc²x

cot x = cos x / sin x, quotient rule, simplify

Exponentials & Logs

100

Derivative of f(x) = (1/3)^{x^2}

2x*ln(1/3)*(1/3)^{x^2}

200

Derivative of f(w) = e^4w/w

(e^4w(4w - 1)) / w²

300

Derivative of g(t) = ln(sin t²)

2t(cot t²)

400

The value of an investment at time t is given by v(t) = 40e^0.4t. Find the instantaneous percentage rate of change.

40%

500

Find the derivative of f(x) = (sin x)^x

xcotx +ln(sinx)

Implicit Diff & Trig Inv

100

Find the slope of the tangent line to y - 3x²y = cosx at (0,1)

0

200

Find y' in y²*sqrt(x+y) - 4x² = y

Numerator: 16x*sqrt(x+y)-y²
Denominator: y² + 4y(x+y) - 2*sqrt(x+y)

300

Given (d/dx)sin^-1x = 1/sqrt(1 - x²), find he derivative of sin^-1(x³+1)

3x² / sqrt(1-(x³+1)²)

400

Find the equation of the tangent line to x²y² = 3y + 1 at the point (2,1)

y - 1 = (-4/5)*(x - 2)

500

Find the derivative of 4sec(x⁴)

16x³sec(x⁴)tan(x⁴)