Review for Quiz

Chain Rule

100

What is the derivative of f(x) = (3x+1)²?

2(3x+1)(3)

200

y = cot(3t), what's y'??

-csc²(3t)(3)

300

f(x) = (6x²+7x)⁴ , f'(x) = 

4(6x²+7x)(12x + 7)

400

What's the derivative of sin(3t) / (1+t²)

[3cos(3t)(1+t²) - (2t)sin(3t) ] / (1+t²)²

500

What's the derivative of g(w) = cos(3w)sec(1-w) ? 

-3sin(3w)sec(1-w) - cos(3w)sec(1-w)tan(1-w)

Implicit Diff.

100

Find y' given that y² + x² = 1?

-x/y

200

Find dy/dx if 1/y + 1/x² = 1

-2y²/x³

300

y = sin(3x + 4y). Find y'

[ 3cos(3x + 4y) ] / [ 1 - 4cos(3x+4y)]

400

Find y' for x³y⁵ + 3x = 8y³+1.

(3x²y⁵+3) / (24y²-5x³y⁴)

500

If y = sin(3x + 4y), y'= 

[ 3cos(3x+4y) ] / [ 1 - 4cos(3x+4y) ]

Mixed

100

y = sin(3t), what's y'?

3cos(3t)

200

Find y' for x³+y³ = 4.

- x²/y²

300

Find y' for y = (4x+x^-5)^1/3

(1/3)(4x+x^-5)^-2/3(4-5x^-6)

400

Find the slope of the curve x²y + y⁴ = 4 + 2x at the point (-1, 1). 

4/5

500

h(z) = tan⁴(z²+1), h'(z) = 

Tip: How many functions can you see that composed gets you h(z)?

4tan³(z²+1)sec²(z²+1)(2z)