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Derivative Review

Authored by HALEY PICHLER

Mathematics

11th Grade - University

CCSS covered

Used 8+ times

Derivative Review
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15 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Find the derivative of
 f(x)=−23x3−12x2+9xf\left(x\right)=-\frac{2}{3}x^3-\frac{1}{2}x^2+9x  

 −2x2−x+9-2x^2-x+9  

 −2x3−x2+9x-2x^3-x^2+9x  

 −212x4−16x3+9 2x2-\frac{2}{12}x^4-\frac{1}{6}x^3+\frac{9}{\ 2}x^2  

 −2x4−x3+9x2-2x^4-x^3+9x^2  

2.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Find the second derivative of the function f(x)=2x−5x6f\left(x\right)=2x-5x^6  

 2−30x52-30x^5  

 x2−57x7x^2-\frac{5}{7}x^7  

 −30x5-30x^5  

 −150x4-150x^4  

3.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

 ddx[sin⁡(x3−2x)]=\frac{d}{dx}\left[\sin\left(x^3-2x\right)\right]=  

 (3x2−2)cos⁡(x3−2x)\left(3x^2-2\right)\cos\left(x^3-2x\right)  

 −(3x2−2)cos⁡(x3−2x)-\left(3x^2-2\right)\cos\left(x^3-2x\right)  

 cos⁡(3x2−2)\cos\left(3x^2-2\right)  

 sin⁡(3x2−2)\sin\left(3x^2-2\right)  

4.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Find the derivative of 
 f(x)=ln⁡(cos⁡(5x2))f\left(x\right)=\ln\left(\cos\left(5x^2\right)\right)  

 1cos⁡(5x2)\frac{1}{\cos\left(5x^2\right)}  

 −(10x sin⁡(5x2)) cos⁡(5x2)-\frac{\left(10x\ \sin\left(5x^2\right)\right)}{\ \cos\left(5x^2\right)}  

 −110xsin⁡(5x2)-\frac{1}{10x\sin\left(5x^2\right)}  

 −sin⁡(5x2)cos⁡(5x2)\frac{-\sin\left(5x^2\right)}{\cos\left(5x_{ }^2\right)}  

5.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Find an equation of the tangent line to the graph of f(x) at the point (1, 100)
f(x) = (5x5 + 5)2

y = 500x + 400
y = 100x + 400
y = -500 x - 400
y = 500x - 400

6.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Find dy/dx by Implicit Differentiation
2/y = x2

-4/x3
x3
1/x2
2/x2

7.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Find the derivative:
y=5x2e3x

y'=10xe3x(2x+3)
y'=5xe3x(3x+2)
y'=10ex3x(3x+2)
y'=5xe3x(2x+3)

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