MAT 136 STUDY GUIDE EXAM 2026 QUESTIONS WITH SOLUTIONS GRADED A+

MAT 136 STUDY GUIDE EXAM 2026
QUESTIONS WITH SOLUTIONS GRADED A+


◉ d/dx (x). Answer: 1


◉ Power Rule: d/dx (x^n). Answer: nx^(n-1)


◉ Sum/Diff Rule: d/dx (f(x) +/- g(x)). Answer: f'(x) +/- g'(x)


◉ Constant Multiple Rule: d/dx (c*f(x)). Answer: c*f'(x)


◉ Product Rule: d/dx (f(x)g(x)). Answer: f'(x)g(x)+f(x)g'(x)


◉ Quotient Rule: d/dx (f(x)/g(x)). Answer: (g(x)f'(x)-f(x)g'(x))/g(x)^2
OR (low dhigh - high dlow)/lowlow


◉ Chain Rule: d/dx f(g(x)). Answer: f'(g(x))g'(x)


◉ Chain Rule w Differentials: dy/dx. Answer: dy/du * du/dx

, ◉ d/dx sin(x). Answer: cos(x)


◉ d/dx 4t^pi. Answer: 0


◉ d/dx sec(x). Answer: sec(x)tan(x)


◉ d/dx tan^-1(x). Answer: 1/1+x^2


◉ d/dx cos(x). Answer: -sin(x)


◉ Higher Order: d/dx (d/dx (f(x))). Answer: f"(x)


◉ d/dx ln(x). Answer: 1/x


◉ d/dx e^x. Answer: e^x


◉ d/dx n^x. Answer: n^x ln(n)


◉ d/dx -sin(x). Answer: -cos(x)


◉ d/dx -cos(x). Answer: sin(x)