Differential Calculus Questions for NDA

Free, AI-curated practice for the Differential Calculus section of NDA. We have 15+ verified questions in this bank. Below: 5 sample questions. Sign up free to unlock unlimited practice + AI explanations + per-topic analytics.

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Sample questions

Q1 · medium · AI-verified

The second derivative of f(x) = x⁴ - 4x³ + 6x² is:

12x² - 24x + 12
4x³ - 12x² + 12x
12x² - 12x + 6
6x² - 12x + 12

Q2 · medium · AI-verified

If y = (x + 1)/(x - 1), then dy/dx equals:

-2/(x-1)²
2/(x-1)²
-1/(x-1)²
1/(x-1)²

Q3 · medium · AI-verified

If f(x) = sin⁻¹(x), then f'(x) equals:

1/√(1-x²)
-1/√(1-x²)
1/√(1+x²)
-1/√(1+x²)

Q4 · medium · AI-verified

The derivative of f(x) = sin(2x) · cos(3x) with respect to x is:

cos(2x)cos(3x) - sin(2x)sin(3x)
2cos(2x)cos(3x) - 3sin(2x)sin(3x)
2sin(2x)cos(3x) - 3cos(2x)sin(3x)
2cos(2x)cos(3x) + 3sin(2x)sin(3x)

Q5 · medium · AI-verified

If f(x) = |x|, then f'(0) is:

0
1
-1
does not exist

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Differential Calculus Questions for NDA

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