What should you do first when solving this problem?

Divide the denominator into each numerator term

Givenf\left(x\right)=3x^2-1, find f'(0) and explain what it means

f'(0) = 0 --> The curve has a vertex

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Calc: Inv 2.2 - Basic Derivatives

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#maths #calculus #derivatives

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Questions 15

Answers

1
Find the derivative of y = \frac{4x^3-10x^2+x}{x}
y' = OMG NOOOOOO
y' = 4x2 - 10x + 1
y' = 12x2 - 20x + 1
y' = 8x - 10
2
Which type of function can you NOT use the Power Rule to differentiate?
Exponentials
Polynomials
Radicals
Inverse
3
what is the derivative of y = 3/x²
y' = -6x
y' = -6/x3
y' = -6/x
y' = 3/(2x)3
4
y = 5sinx - 10cosx
y' = -5cosx - 10sinx
y' = 5cosx - 10sinx
y' = -5cosx + 10sinx
y' = 5cosx + 10sinx
5
What should you do first when solving this problem?
Take the power rule
Multiply the exponents with the coefficients
Plug in the given x-value
Divide the denominator into each numerator term
6
Which of the following is INCORRECT when using the power rule?
Multiply the power by the coefficient first
x's need to be seperated by +/-'s in the numerator
You can use it for decimal and negative exponents
Subtract the power by 1 first
7
Which function cannot be differentiated with the Power Rule?
sin2x
1/x
x1/3
x-5
8
What is the derivative of ....
8x1/3
6x4/3
8x(17/3)
6x1/3
9
Givenf\left(x\right)=3x^2-1, find f'(0) and explain what it means
f'(0) = 0 --> The entire curve is a horizontal line
f'(0) = 0 --> The curve has a vertex
f'(0) = -1 --> The curve is decreasing moderately
f'(0) = - 1 --> The curve is increasing moderately
10
Which function turns negative when you take its derivative?
cosx
sinx
ex
any constant
11
What is the derivative of y = 4x³ + 3x + 1
y' = 4x2 + 3
y' = 4x2 + 3x
y' = 12x + 3x
y' = 12x2 + 3
12
Find the derivative of y = x²x⁵
y' = 10xx4
y' = 25x6
Can't use the power rule
y' = 7x6
13
Which of the following is NOT a part of differentiating a radical or inverse function?
Simplify so there's no fractional or negative exponents
Differentiate using the power rule
Rewrite to x's being raised to a power
Use the 3 special derivatives
14
What is the derivative of y = 5e^x - 10x + 6
y' = 5ex
y' = 5ex - 10
y' = 5ex - 16
y' = 5x*ex - 10
15
Given f(x) = 2x⁵ - 7x, determine its slope when x = -1
f(-1) = 5
f'(-1) = 167
f'(-1) = 3
f'(x) = 10x4 - 7

Calc: Inv 2.2 - Basic Derivatives Flashcards | StudBud

Calc: Inv 2.2 - Basic Derivatives

15 termsStudBud Administration318 plays

#maths #calculus #derivatives

Flashcards15 cardsFPractice quizPHost liveL

Questions 15

Answers

1
Find the derivative of y = \frac{4x^3-10x^2+x}{x}
y' = OMG NOOOOOO
y' = 4x2 - 10x + 1
y' = 12x2 - 20x + 1
y' = 8x - 10
2
Which type of function can you NOT use the Power Rule to differentiate?
Exponentials
Polynomials
Radicals
Inverse
3
what is the derivative of y = 3/x²
y' = -6x
y' = -6/x3
y' = -6/x
y' = 3/(2x)3
4
y = 5sinx - 10cosx
y' = -5cosx - 10sinx
y' = 5cosx - 10sinx
y' = -5cosx + 10sinx
y' = 5cosx + 10sinx
5
What should you do first when solving this problem?
Take the power rule
Multiply the exponents with the coefficients
Plug in the given x-value
Divide the denominator into each numerator term
6
Which of the following is INCORRECT when using the power rule?
Multiply the power by the coefficient first
x's need to be seperated by +/-'s in the numerator
You can use it for decimal and negative exponents
Subtract the power by 1 first
7
Which function cannot be differentiated with the Power Rule?
sin2x
1/x
x1/3
x-5
8
What is the derivative of ....
8x1/3
6x4/3
8x(17/3)
6x1/3
9
Givenf\left(x\right)=3x^2-1, find f'(0) and explain what it means
f'(0) = 0 --> The entire curve is a horizontal line
f'(0) = 0 --> The curve has a vertex
f'(0) = -1 --> The curve is decreasing moderately
f'(0) = - 1 --> The curve is increasing moderately
10
Which function turns negative when you take its derivative?
cosx
sinx
ex
any constant
11
What is the derivative of y = 4x³ + 3x + 1
y' = 4x2 + 3
y' = 4x2 + 3x
y' = 12x + 3x
y' = 12x2 + 3
12
Find the derivative of y = x²x⁵
y' = 10xx4
y' = 25x6
Can't use the power rule
y' = 7x6
13
Which of the following is NOT a part of differentiating a radical or inverse function?
Simplify so there's no fractional or negative exponents
Differentiate using the power rule
Rewrite to x's being raised to a power
Use the 3 special derivatives
14
What is the derivative of y = 5e^x - 10x + 6
y' = 5ex
y' = 5ex - 10
y' = 5ex - 16
y' = 5x*ex - 10
15
Given f(x) = 2x⁵ - 7x, determine its slope when x = -1
f(-1) = 5
f'(-1) = 167
f'(-1) = 3
f'(x) = 10x4 - 7