Differentiation Quiz - MCQ Questions with Solutions (original) (raw)

If f(x) = (x^2 + 1)/(x + 1), what is f'(x)?

If f(x) = sqrt(x)sin(x), what is f''(x), the second derivative?

• sqrt(x)cos(x) - 2sin(x)/√(x)
• sqrt(x)cos(x) + 2sin(x)/√(x)
• sqrt(x)cos(x) - sin(x)/√(x)
• sqrt(x)cos(x) + sin(x)/√(x)

If g(x) = ln(2e^(-x) + 3), what is g'(x)?

If h(x) = sin^2(x)e^x, what is h''(x), the second derivative?

• 2e^(sin^2(x))cos(x)sin(x)

If f(x) = x^3 + 2x^2 - 4x + 1, what is the absolute minimum value of f(x)?

If f(x) = x^3 - 4x^2 + 5x + 2, what is the interval where f(x) is concave upward?

If h(x) = x^3e^(-2x^2), what is h''(x), the second derivative?

• -4x^3e^(-2x^2) - 12xe^(-2x^2)
• -6x^2e^(-2x^2) + 4x^4e^(-2x^2)
• 6x^2e^(-2x^2) - 4x^4e^(-2x^2)
• Apply the product rule twice.4x^3e^(-2x^2) + 12xe^(-2x^2)

If h(x) = ln(1 + e^(-2x)), what is h'(x)?

If h(x) = 2x^3 - 5x^2 + 3, what is the point(s) of inflection?

What is the derivative of ln(1 + e^(-x))?

There are 25 questions to complete.

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