1.
Differentiate y= 4x-5
Correct Answer
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.
2.
Differentiate y= -x+4x^{2}
Correct Answer
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.
3.
Differentiate y =(2-4x)^{4}
Correct Answer
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.
4.
Differentiate y=2(4-x)^{5}
Correct Answer
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.
5.
Differentiate y= (12+3x)^{4}
Correct Answer
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.
6.
Differentiate y=(2-x)^{6}?
Correct Answer
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.
7.
Is differentiation of y=(3x-1)^{3} is 3(3x-1)^{2} true or false?
Correct Answer
B. False
Explanation
The given statement is false. The correct differentiation of y=(3x-1)^3 is 3(3x-1)^2.
8.
Differentiate y=-5x^{3}+4x^{2}-x
Correct Answer
D. -15x^{2}+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.