f′Field Guide
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Math 190 · your packet

Practice quiz, solved step by step

All 18 questions from your study packet. Time target: 50–60 minutes. Try each one on paper first, then open the steps. The tag on each question links to the lesson below that teaches it.

0 / 18 problems mastered
2.8 priority

1, 3, 7, 11, 21, 25, 29, 31

3.1 priority

3, 9, 15, 23, 31, 39, 59, 65, 71

3.2 priority

3, 9, 15, 21, 29, 37, 43

3.3 priority

1, 7, 13, 19, 27, 35, 45, 53, 59

3.4 priority

1, 9, 17, 25, 33, 41, 49, 57, 61

3.5 priority

1, 5, 11, 17, 23, 29, 35, 53, 55

Q1 · §2.8 →
Use the limit definition to find f′(x)f'(x) for f(x)=x2+3xf(x)=x^2+3x.
Q2 · §2.8 →
Find the slope of the tangent line to f(x)=x2−4xf(x)=x^2-4x at x=3x=3.
Q3 · §2.8 →
At what value is f(x)=∣x−2∣f(x)=|x-2| not differentiable? Explain.
Q4 · §3.1 →
Differentiate y=7x5−4x3+6x−9y=7x^5-4x^3+6x-9.
Q5 · §3.1 →
Differentiate y=5ex+3(2x)−8x2y=5e^x+3(2^x)-\dfrac{8}{x^2}.
Q6 · §3.1 →
Find the tangent line to y=x3−2xy=x^3-2x at x=1x=1.
Q7 · §3.2 →
Differentiate y=(x2+1)(x3−2x)y=(x^2+1)(x^3-2x).
Q8 · §3.2 →
Differentiate y=x2+3x−1y=\dfrac{x^2+3}{x-1}.
Q9 · §3.2 →
Differentiate y=x2exy=x^2e^x.
Q10 · §3.3 →
Differentiate y=3sin⁡x−2cos⁡x+tan⁡xy=3\sin x-2\cos x+\tan x.
Q11 · §3.3 →
Differentiate y=xsin⁡xy=x\sin x.
Q12 · §3.3 →
Find y′(0)y'(0) if y=sin⁡x1+cos⁡xy=\dfrac{\sin x}{1+\cos x}.
Q13 · §3.4 →
Differentiate y=(3x2−1)5y=(3x^2-1)^5.
Q14 · §3.4 →
Differentiate y=sin⁡(x3+2x)y=\sin(x^3+2x).
Q15 · §3.4 →
Differentiate y=e4x2−3xy=e^{4x^2-3x}.
Q16 · §3.5 →
Find dy/dxdy/dx if x2+y2=25x^2+y^2=25.
Q17 · §3.5 →
Find dy/dxdy/dx if x2y+y3=7x^2y+y^3=7.
Q18 · §3.5 →
Find the slope of the tangent line to x2+xy+y2=7x^2+xy+y^2=7 at (1,2)(1,2).