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# Derivatives Questions - All Grades

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Differentiate. $f(x) = 3x^5 - 2x^2 - 7x^(-3) + 9x^(-4)$
1. $f(x) = 15x^4 - 4x - 21x^(-2) + 36x^(-3)$
2. $f(x) = 15x^4 - 4x + 21x^(-4) - 36x^(-5)$
3. $f(x) = 15x^4 - 4x + 21x^(2) - 36x^(5)$
4. $f(x) = 15x^4 - 4x - 21x^(-4) + 36x^(-5)$
What is the derivative of $f(x) = 3x^2 - x + 8 ?$
1. $f'(x)=6x-1$
2. $f'(x)=6x+8$
3. $f'(x) = 3x$
4. $f'(x)=9x+7$
What is the derivative of $f(x)=23pi ?$
1. $f'(x) = 23pi$
2. $f'(x) = pi$
3. $f'(x) = 0$
4. $f'(x) = 23$
What is the derivative of $f(x) = 2sqrt(x^7) - 5root[4](x^3) + 9root[3](x^2) - 6/root[6](x^5)?$
1. $f'(x) = x^3 - 5/2 sqrt(x) + 9/2root[6](x) + 3/root[3](x^4)$
2. $f'(x) = 7sqrt(x^5) - 20/(3root[4](x)) + 3/(2root[3](x)) - 5/root[6](x^11)$
3. $f'(x) = 7sqrt(x^5) - 15/(4root[4](x)) + 6/root[3](x) + 5/root[6](x^11)$
4. $f'(x) = 14x^3 - 15sqrt(x)+ 18root[3](x) + 30/root[3](x^2)$
What is the derivative of $f(x)=3x^4 ?$
1. $f'(x)=3x^3$
2. $f'(x)=12x$
3. $f'(x)=12x^3$
4. $f'(x)=4x$
Find the derivative. $f(x) = 4sqrt(x)+3$
1. $f'(x) = 4/sqrt(x)$
2. $f'(x) = 4/sqrt(x) + 1/3$
3. $f'(x) = 2$
4. $f'(x) = 2/sqrt(x)$
Find the derivative. $f(x)=99x$
1. $f'(x) = 99$
2. $f'(x) = x$
3. $f'(x) = 99x$
4. $f'(x) = 100$
Differentiate. $f(x)=2x^6$
1. $f'(x) = 6$
2. $f'(x) = 6x^5$
3. $f'(x) = 12x^5$
4. $f'(x) = 12$
Calculate the derivative. $f(x)=8x^2-5x+3$
1. $f'(x) = 8x$
2. $f'(x) = 16x-5x$
3. $f'(x) = 2x-5$
4. $f'(x) = 16x-5$
On what intervals is the function $f(x)=3x^3+2x^2$ concave upwards and downwards?
1. concave upward $(-2/9, oo)$, concave downward $(-oo, -2/9)$
2. concave upward $(-oo, -2/9)$, concave downward $(-2/9, oo)$
3. concave upward $(0, oo)$, concave downward $(-oo, 0)$
4. concave upward $(-oo, 0)$, concave downward $(0, oo)$
Find the derivative. $f(x) = 4x^3 - 3sqrt(x^3) + sqrt(x)$
1. $f'(x) = 12x^2 - 9/2 sqrt(x) + 1/(2sqrt(x))$
2. $f'(x) = 12x^2 + 2/(sqrt(x))$
3. $f'(x) = 4x^2 - 9sqrt(x) + 1$
4. $f'(x) = 64x^2 + 9sqrt(x) - 1/sqrt(x)$
What is the derivative of $f(x)=sin(3x^2) ?$
1. $f'(x)=3x^2cos(3x^2)$
2. $f'(x)=6xcos(3x^2)$
3. $f'(x)=3x^2sin(3x^2)$
4. $f'(x)=6xsin(3x^2)$
Find the derivative. $f(x)=5x^2−6x+4$
1. $f'(x) = 10x - 6$
2. $f'(x) = 5x - 6$
3. $f'(x) = 25x$
4. $f'(x) = 7x - 5$
What is the second derivative of $f(x)=3x^3+2x^2$?
1. $f''(x)=18x+4$
2. $f''(x)=9x^2+4x$
3. $f''(x)=18$
4. $f''(x)=0$
Identify the intervals on which the given function is increasing and decreasing.
$f(x)=x^3+x^2-x$
1. Increasing: $(-oo, -1) uu (1/3,oo)$; decreasing: $(-1, 1/3)$
2. Increasing: $(-oo, -1)$; decreasing: $(-1, 1/3)$
3. Increasing for all x
4. Increasing: $(-1,1/3)$; decreasing: $(-oo, -1) uu (1/3,oo)$
On $f(x)=2x^5+x^3-3x$
1. $(-0.65,1.4)$ is a relative and absolute maximum.
2. $(0.65,-1.4)$ is a relative and absolute minimum.
3. $(-0.65,1.4)$ is a relative maximum.
4. $(0.65,-1.4)$ is a relative minimum.
5. Both A and B.
6. Both C and D.
7. None of the above.
What is the derivative of $f(x)=3x^3+2x^2$?
1. $f'(x)=9x^2+4x$
2. $f'(x)=3x^2+2x$
3. $f'(x)=0$
4. $f'(x)=12x^2+6x$
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