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
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
