alleryStart learning →What is the derivative of x^5 with respect to x?
- 4x^5
- 5x^5
- x^4
- 5x^4
Show answer and solution
Correct answer: D. 5x^4
Power rule: bring the exponent 5 down and reduce the power by one, giving 5x^4.
CA Foundation Basic Differential and Integral Calculus — practice questions
Explore 65 free Basic Differential and Integral Calculus questions in CA Foundation Quantitative Aptitude. Open each question or exercise to read its content, reference answers and available explanation.
Practise Basic Differential and Integral Calculus with Quill →Basic Differential and Integral Calculus questions and exercises with answers
Showing questions 1–30 of 65.
What is the derivative of x^5 with respect to x?Read the answer and worked solution →What is the derivative of the constant function f(x) = 7?Read the answer and worked solution →Differentiate y = 3x^2 + 4x with respect to x.Read the answer and worked solution →Find d/dx of x ln x for x > 0.Read the answer and worked solution →Using the quotient rule, d/dx of x/(x+1) equalsRead the answer and worked solution →By the chain rule, the derivative of (2x+3)^4 isRead the answer and worked solution →What is d/dx of 1/x for x not equal to 0?Read the answer and worked solution →What is the second derivative of f(x) = x^4?Read the answer and worked solution →For f(x) = 5x^3 - 2x, the second derivative at x = 1 equalsRead the answer and worked solution →What is the slope of the tangent to y = x^2 - 4x at x = 1?Read the answer and worked solution →The function f(x) = x^2 - 8x + 3 has f'(x) = 0 at x equal toRead the answer and worked solution →A body moves so that s = t^2 + 3t. Its velocity at t = 2 isRead the answer and worked solution →Which mathematician introduced the dy/dx form of derivative notation?Read the answer and worked solution →In Newton's dot notation, a dot placed over a symbol stands forRead the answer and worked solution →Geometrically, the derivative of a function at a point gives theRead the answer and worked solution →The process of finding a derivative is calledRead the answer and worked solution →An antiderivative of a function f is a function thatRead the answer and worked solution →A partial derivative differentiates in one variable whileRead the answer and worked solution →For a differentiable function, interior local extrema occur only atRead the answer and worked solution →Higher-order derivatives are obtained byRead the answer and worked solution →Total cost is C = 500 + 20x + 0.5x^2. Marginal cost at x = 10 isRead the answer and worked solution →If a firm's fixed cost doubles, its marginal costRead the answer and worked solution →Revenue is R = 50x - 0.5x^2. Marginal revenue at x = 20 isRead the answer and worked solution →A firm sells at a fixed price of 40 per unit, so R = 40x. Its MR isRead the answer and worked solution →Revenue is R = 100x - 2x^2. What is the maximum revenue?Read the answer and worked solution →Profit is P = -x^2 + 60x - 200. What is the maximum profit?Read the answer and worked solution →A profit-maximising firm chooses the output whereRead the answer and worked solution →Cost is C = x^2 + 10x + 400. The minimum average cost isRead the answer and worked solution →For C = x^2 + 10x + 400, average cost is least at outputRead the answer and worked solution →When marginal cost lies below average cost, average costRead the answer and worked solution →
Worked practice questions
What is the derivative of the constant function f(x) = 7?
- 1
- 7
- 7x
- 0
Show answer and solution
Correct answer: D. 0
A constant does not change with x, so its rate of change is zero.
Differentiate y = 3x^2 + 4x with respect to x.
- 3x+4
- x^3+2x^2
- 6x^2+4
- 6x+4
Show answer and solution
Correct answer: D. 6x+4
Term by term, 3x^2 gives 6x and 4x gives 4, so dy/dx = 6x + 4.
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