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Calculus
Test Description: Derivatives
Instructions: Answer all questions to get your test result.
1) Using NATURAL LOGARITHMIC FUNCTION. What is the derivative of Dx ln cos(〖3x〗^2-2x+55).
A
(6x-2)(tan〖3x〗^2-2x+5)
B
(-6x+2)(tan〖3x〗^2-2x+5)
C
(2-6x)(tan〖3x〗^2-2x+5)
D
(-2+6x)(tan〖3x〗^2-2x+5)
2) Using NATURAL LOGARITHMIC FUNCTION. What is the derivative of Dx ln 〖cos〗^4 (〖3x〗^2-2x+5).
A
8(3x+1)tan(〖3x〗^2-2x+5)
B
-8(3x+1)tan(〖3x〗^2+2x-5)
C
8(3x-1)tan(〖3x〗^2+2x+5)
D
-8(3x-1)tan(〖3x〗^2-2x+5)
3) Using TRIGONOMETRIC FUNCTION . What is the derivative of F(x) = 3secx tanx.
A
(3-3sin^2)/(sin^3 x)
B
(3+3sin^2)/(cos^3 x)
C
(3+3sec^2)/(sec^3 x)
D
(3-3sin^2)/(cos^3 x)
4) Using TRIGONOMETRIC FUNCTION . What is the derivative of f(x) = x^2 cosx-2x sinx - 2cosx
A
x^2 cosx
B
-x^2 sinx
C
x^2 cosx
D
x^2 sinx
5) Using COMPOSITE FUNCTION. What is the derivative of y = cos (3x^2-2x+5).
A
(6x+2) sin ( 3x^2-2x+5)
B
(6x-2) sin ( 3x^2+2x-5)
C
(6x-2) sin ( 3x^2-2x+5)
D
(6x+2) cos ( 3x^2-2x+5)
6) Using COMPOSITE FUNCTION. What is the derivative of y = tan ((3-x)/(x^2-2)).
A
(x-6x+2)/((〖x^2-2)〗^2 )
B
(x+6x+2)/((〖x^2+2)〗^2 )
C
(x-6x+2)/((〖x^2+2)〗^2 )
D
(x+6x-2)/((〖x^2-2)〗^2 )
7) Using Power rule. Find the derivative of y = 7 x4
A
-28x^2
B
-28x^3
C
28x^3
D
28x^2
8) Using Power rule. Find the derivative of y = 2 x^3 - 4 x^2 + 3 x - 5
A
-6x^2-8x+3
B
6x^2-8x+3
C
8x^2-8x+3
D
-8x^2-8x+3
9) Using Power rule. Find the derivative of y = x^2+x^3
A
-3x + 3x^2
B
-2x + 3x^2
C
2x + 3x^2
D
3x + 3x^2
10) Using Power rule. Find the derivative of y = v3 - v4
A
3v^2 - 4v^3
B
-4v^2 - 3v^3
C
-3v^2 - 4v^3
D
4v^2 - 3v^3
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