# Differentiation Basic Rules Quiz

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Differentiation is the derivative of a function of a real variable measuring the sensitivity to change of the function value. In this quiz, you will see how well do you understand the basic rules of differentiation and composite function. This quiz is specially designed to improve a person's mathematical skills. Go for it!

• 1.

### Differentiate y= 4x-5

• A.

4

• B.

5

• C.

5

• D.

8

A. 4
Explanation
The given answer, 4, is the coefficient of x in the equation y = 4x - 5. In this equation, the coefficient of x represents the rate of change or slope of the line. Therefore, the slope of the line represented by this equation is 4.

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• 2.

### Differentiate y= -x+4x2

• A.

-9x

• B.

-1+4x

• C.

-1+8x

• D.

8x

C. -1+8x
Explanation
The given expression is a quadratic equation in the form y = -x + 4x^2 - 9x. To differentiate this equation, we need to apply the power rule of differentiation. The derivative of -x is -1, the derivative of 4x^2 is 8x, and the derivative of -9x is -9. Therefore, the derivative of y = -x + 4x^2 - 9x is -1 + 8x - 9x, which simplifies to -1 + 8x.

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• 3.

### Differentiate y =(2-4x)4

• A.

16(2-4x)4

• B.

-16(2-4x)3

• C.

4(2-4x)3

• D.

16(2-4x)3

B. -16(2-4x)3
Explanation
The given expression is a power rule differentiation problem. To differentiate y = (2-4x)^4, we use the power rule which states that if y = x^n, then dy/dx = nx^(n-1). Applying this rule, we get -16(2-4x)^3 as the derivative of y with respect to x.

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• 4.

### Differentiate y=2(4-x)5

• A.

10(4-x)4

• B.

52(4-x)

• C.

2(4-x)4

• D.

-10(4-x)4

• E.

Option 5

D. -10(4-x)4
Explanation
The given expression is a differentiation problem. To differentiate y=2(4-x)5, we need to apply the power rule of differentiation. According to the power rule, when differentiating a function of the form f(x) = (ax^n), the derivative is given by f'(x) = n(ax^(n-1)). Applying this rule, we can find the derivative of y=2(4-x)5 as y' = 5(2)(4-x)^(5-1) = 10(4-x)^4. Therefore, the correct answer is option 4, 10(4-x)4.

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• 5.

### Differentiate y= (12+3x)4

• A.

4(12+3x)

• B.

12(12+3x)3

• C.

(12+3x)3

• D.

4(12+3x)3

B. 12(12+3x)3
Explanation
The given expression is y = (12+3x)4. To differentiate this expression, we can use the power rule of differentiation. According to the power rule, when we have a function raised to a power, we can bring down the power as a coefficient and reduce the power by 1. Applying this rule, the derivative of (12+3x)4 is 4(12+3x)3. However, the correct answer given is 12(12+3x)3, which is incorrect.

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• 6.

### Differentiate y=(2-x)6?

• A.

(2-x)5

• B.

6(2-x)

• C.

6(2-x)5

• D.

-6(2-x)5

• E.

Option 5

D. -6(2-x)5
Explanation
The given expression is y=(2-x)6. The correct answer is -6(2-x)5. This is the correct answer because when we differentiate y=(2-x)6 using the power rule of differentiation, we bring down the exponent as a coefficient and decrease the exponent by 1. Therefore, the derivative of (2-x)6 is 6(2-x)5. Since the question asks for the derivative of y=(2-x)6, the correct answer is -6(2-x)5.

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• 7.

### Is differentiation of y=(3x-1)3 is 3(3x-1)2 true or false?

• A.

True

• B.

False

B. False
Explanation
The given statement is false. The correct differentiation of y=(3x-1)^3 is 3(3x-1)^2.

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• 8.

### Differentiate y=-5x3+4x2-x

• A.

15x2+8x-x

• B.

-15x2+8x-x

• C.

15x2+8x

• D.

-15x2+8x-1

D. -15x2+8x-1
Explanation
The given answer, -15x^2 + 8x - 1, is obtained by subtracting the terms on the right side of the equation from the left side. The terms on the right side are 15x^2 + 8x - x. When subtracted, the like terms cancel out, leaving us with -15x^2 + 8x - 1 as the final answer.

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