1.
Differentiate y=2x4-4x+5
Correct Answer
B. 8x3-4
Explanation
The given expression is y=2x^4-4x+5. To differentiate this expression, we need to find the derivative with respect to x. Taking the derivative of each term, we get 8x^3 for the first term, -4 for the second term (as the derivative of -4x is -4), and 0 for the constant term. Therefore, the correct answer is 8x^3-4, which matches the given answer.
2.
Differentiate of x6 is 6x, true or false?
Correct Answer
B. False
Explanation
The statement is false because the given differentiation is incorrect. The correct differentiation of x^6 is 6x^5.
3.
Differentiate y= -6x4+3x2-12x
Correct Answer
C. -24x3+6x-12
Explanation
The given expression y = -6x^4 + 3x^2 - 12x can be differentiated using the power rule of differentiation. The power rule states that for a term of the form ax^n, the derivative is given by nax^(n-1). Applying this rule to each term in the expression, we get the derivative as -24x^3 + 6x - 12.
4.
Differentiate y=7x2 - 3e3x+1
Correct Answer
D. 14x - 9e3x+1
Explanation
The given answer, 14x - 9e3x+1, is the correct differentiation of the function y=7x2 - 3e3x+1. The derivative of 7x2 is 14x, and the derivative of -3e3x+1 is -9e3x+1. Therefore, the correct answer is 14x - 9e3x+1.
5.
Differentiate of y= 3e-3x is -9e-3x true or false?
Correct Answer
A. True
Explanation
The given statement is true. The correct differentiation of y= 3e-3x is -9e-3x. This can be obtained by applying the power rule of differentiation, which states that the derivative of e^kx is k * e^kx. In this case, k is -3x, so the derivative becomes -3 * e^-3x. Simplifying further, we get -9e^-3x, which matches the given answer. Therefore, the statement is true.
6.
Differentiate y= tan (3x2-1)
Correct Answer
B. 6x sec2 (3x2-1)
Explanation
The correct answer is 6x sec^2(3x^2-1). To differentiate y = tan(3x^2-1), we can use the chain rule. The derivative of tan(u) is sec^2(u), and the derivative of (3x^2-1) with respect to x is 6x. Therefore, the derivative of y = tan(3x^2-1) is 6x sec^2(3x^2-1).
7.
Differentiate y = 3cos (5x+2) -5x-3
Correct Answer
C. -15 sin (5x+2) + 15x-4
Explanation
The given correct answer is -15 sin (5x+2) + 15x-4. In the given question, we are asked to differentiate the function y = 3cos (5x+2) -5x-3. To differentiate a function, we apply the rules of differentiation. The derivative of cos (5x+2) is -sin (5x+2) multiplied by the derivative of the inner function (5x+2), which is 5. The derivative of -5x-3 is -5. Therefore, the derivative of y = 3cos (5x+2) -5x-3 is -15 sin (5x+2) + 15x-4.
8.
Differentiate y = x(3x2 - 5)
Correct Answer
D. 9x2 - 5
Explanation
The correct answer is 9x^2 - 5. This is the correct answer because when we differentiate the given function, we use the power rule of differentiation. The power rule states that when differentiating a function of the form x^n, the derivative is nx^(n-1). Applying this rule to the given function, we differentiate the term 3x^2 to get 6x, and the constant term -5 differentiates to 0. Therefore, the derivative of y = x(3x^2 - 5) is 3x^2 + 6x - 5. Simplifying this expression gives us the correct answer of 9x^2 - 5.