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CALCULUS DERIVATIVE RULES Questions with Correct Solutions

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CALCULUS DERIVATIVE RULES Questions with Correct Solutions

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CALCULUS: DERIVATIVE RULES Questions with Correct Solutions


Question:
1. d/dx [c], where c is a constant

Answer:
0


Question:
2. d/dx [x]

Answer:
1


Question:
3. d/dx [cx], where c is a constant

Answer:
c


Question:
4. d/dx [x^n]

Answer:
n*x^(n-1)


Question:
5. d/dx [cx^n], where c is a constant

Answer:
cnx^(n-1)


Question:
6. d/dx [f(x)*g(x)] (product rule for f and g)

Answer:
f'(x)*g(x) + g'(x)*f(x)


Question:
7. d/dx [g(x)*h(x)] (product rule for g and
h)

Answer:
g'(x)*h(x)+h'(x)*g(x)

, Question:
8. d/dx [f(x)/g(x)] (quotient rule for f over
g)

Answer:
[f'(x)*g(x)-g'(x)*f(x)] / [(g(x))^2]


Question:
9. d/dx [g(x)/h(x)] (quotient rule for g over
h)

Answer:
[g'(x)*h(x)-h'(x)*g(x)] / [(h(x))^2]


Question:
10. d/dx sin x

Answer:
cos x


Question:
11. d/dx cos x

Answer:
-sin x


Question:
12. d/dx tan x

Answer:
sec^2 x


Question:
13. d/dx cot x

Answer:
-csc^2 x


Question:
14. d/dx sec x

Answer:
sec x * tan x

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