What is the derivative for dy/dx= x2 + 1/x?

f'\left(x\right)=2x-\frac{1}{x^2}

What are derivatives useful for?

To calculate the slope of a curve in different places

What happens to a constant during differentiation? ex) f(x) = 7

The value of the constant will be equal to 0

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Math Derivatives Calculus

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Questions 18

Answers

1
What is the derivative for dy/dx= x² + 1/x?
y = -1/x2
y'=\frac{1}{x^2}
f'\left(x\right)=2x-\frac{1}{x^2}
y '= -1/x2
2
What happens when you have Y= f(x) + g(x)?
Only f(x) is derived
Only g(x) is derived
Both f(x) and g(x) are derived
Neither are derived
3
What is the derivative of f(x)= x⁷
f '(x)= 7x6
f (x)= 6x7
dx/dy= 6x7
f '(x)= 2x6
4
What are the ways to name the derivative?
f '(y), dy/dx, y'
f '(x), dx/dy, y '
f '(x), dy/dx, y'
f (x), dy/dx, y'
5
What is the 2nd derivative of f\left(x\right)=3x^3-4x^2+1
f '(x)= -18x - 8x + 1
f ''(x)= 18x - 8
f''(x) = 9x2 - 8x
f ''(x)= 9x2 - 8
6
What are derivatives useful for?
To calculate the mean of a set of numbers
To calculate the slope of a curve in different places
To find the range of a model
To Calculate the best fit line in a scatter graph
7
What is the second derivative for f(x)= 2x³+9
f''(x) = 12x
f''(x)= 6x3
f''(x) = 3x2
f'(x)= 6x2
8
What is the derivative of f(x)= (2x+3)² ?
y '= 6x + 6
y'=\left(2x+3\right)^2
y' = 8x + 12
y '= 2x -6x2
9
What is the derivative for f(x)= x^-1?
dy/dx= -x2
dy/dx= -x-2
dy/dx= x-2
dx/dy= -x-2
10
What is the derivative ofy=\frac{3}{x^2} ?
y'= -6x-3
y'= -6x3
y'= 6x-3
y= -6x-3
11
What is the derivative for y= 3x²+x-3 ?
f '(x)= 6x2 + 1
f '(x)= 6x-2 + 1
f '(x)= 6x + 3
f '(x)= 6x + 1
12
What is the derivative for dy/dx= x³-4x²?
f '(x)= 3x2 -8x
f (x)= 3x2 -8x
f '(x)= 3x3 -8x
f '(x)= 3x2 -16x
13
What happens to a constant during differentiation? ex) f(x) = 7
The value of the constant will be equal to 1
The value of the constant will be equal to 0
There can not be constants in differentiation
The value of the constant will be the same
14
What rule is used to differentiate power functions?
f '(x)= nXn-1
f '(x)= nXn
f(x)=nXn-1
f'(y)= nXn-1
15
What is the derivative of\frac{dy}{dx}=\sqrt{x}?
f '(x)= 1/2x1/2
f (x)= 1/2x-1/2
f '(x)= -1/2x-1/2
f '(x)= 1/2x-1/2
16
What is the derivative for dy/dx = 1 + 1/x ?
y '= 1/x2
y = -1/x2
y '= x-2
y '= -1/x2
17
What is the answer to dy/dx= X^-4?
f '(x)= -4x5
f '(x)= -5x-4
dy/dx= -4x-5
f (x)= -4x-5
18
What is the derivative of f(x)=5x²?
f'(x)= 10x
y '= 10x2
y= 10x2
dx/dy = 10x

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