Differentiation Basic Rules Quiz

1. Differentiate y= 4x-5

4

5

8

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.

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.

2. Differentiate y= -x+4x²

-9x

-1+4x

-1+8x

8x

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.

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.

3. Differentiate and Match the following

y=5x-1

y=16-2x

y=14-x

y=x+11

Submit

4. Differentiate y=(2-x)⁶?

(2-x)5

6(2-x)

6(2-x)5

-6(2-x)5

Option 5

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.

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.

5. Differentiate y=-5x³+4x²-x

15x2+8x-x

-15x2+8x-x

15x2+8x

-15x2+8x-1

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.

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.

6. Differentiate y= (12+3x)⁴

4(12+3x)

12(12+3x)3

(12+3x)3

4(12+3x)3

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.

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.

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

True

False

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

Explanation

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

8. Differentiate and Match the following:

y=-6x-5

y=6x

y=43-x

y=5+x

Submit

9. Differentiate y =(2-4x)⁴

16(2-4x)4

-16(2-4x)3

4(2-4x)3

16(2-4x)3

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.

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.

10. Differentiate y=2(4-x)⁵

10(4-x)4

52(4-x)

2(4-x)4

-10(4-x)4

Option 5

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.

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.