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Differentiation Practice Questions

JEE · Mathematics · 1600 free MCQs with instant results and detailed explanations.

1600
Total
333
Easy
658
Medium
609
Hard

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Topics in Differentiation

First Principles 290
Chain Rule 222
Product and Quotient Rule 227
Implicit Differentiation 167
Parametric Differentiation 134
Logarithmic Differentiation 324
Higher Order Derivatives 236

Sample Questions from Differentiation

Here are 10 sample questions. Start a quiz to get randomized questions with scoring.

Q1
Easy
What is the derivative of f(x) = x² using first principles?
A. 2x
B. x
C. x²
D. 2
Show Answer & Explanation
Correct Answer: A
Using first principles, the derivative f'(x) = lim(h→0) [(f(x+h) - f(x))/h]. For f(x) = x², this simplifies to 2x.
Q2
Easy
Using first principles, find the derivative of f(x) = 3x + 4.
A. 3
B. 4
C. 0
D. 1
Show Answer & Explanation
Correct Answer: A
The derivative of a linear function is constant. Using first principles, you find the slope equals 3.
Q3
Easy
Find the derivative of f(x) = 1/x using first principles.
A. -1/x²
B. 1/x²
C. 1/x
D. 0
Show Answer & Explanation
Correct Answer: A
Using first principles, the limit yields -1/x² as the derivative.
Q4
Medium
What is the derivative of f(x) = x^3 + 3x^2 - 5x + 4 using first principles?
A. 3x^2 + 6x - 5
B. 3x^2 + 3x - 5
C. 3x^2 + 2x - 5
D. 3x^2 + 6x + 5
Show Answer & Explanation
Correct Answer: A
Using the definition of derivative, we find f'(x) = lim(h->0) [(f(x+h) - f(x))/h]. This gives 3x^2 + 6x - 5.
Q5
Medium
Using the first principles, find the derivative of f(x) = sin(x).
A. cos(x)
B. -sin(x)
C. 1
D. tan(x)
Show Answer & Explanation
Correct Answer: A
The limit process leads to f'(x) = lim(h->0) [(sin(x+h) - sin(x))/h] = cos(x).
Q6
Medium
Evaluate the derivative of f(x) = e^x using first principles.
A. e^x
B. x e^(x-1)
C. xe^x
D. 1
Show Answer & Explanation
Correct Answer: A
Using the limit definition, the derivative of e^x is e^x for all x.
Q7
Medium
Find the derivative of f(x) = ln(x) using first principles.
A. 1/x
B. ln(x)
C. x
D. e^x
Show Answer & Explanation
Correct Answer: A
Applying the limit definition, f'(x) = lim(h->0) [(ln(x+h) - ln(x))/h] = 1/x.
Q8
Hard
If f(x) = x^3 - 6x^2 + 9x, using first principles, what is f'(1)?
A. 0
B. 3
C. 6
D. 9
Show Answer & Explanation
Correct Answer: A
Calculating the derivative using the definition yields f'(1) = 0.
Q9
Hard
Using first principles, find the derivative of f(x) = sin(x) at x = π/4.
A. √2/2
B. 1
C. √3/2
D. 0
Show Answer & Explanation
Correct Answer: A
The limit definition applied here shows that the derivative of sin(x) at π/4 is √2/2.
Q10
Hard
Determine the derivative of f(x) = ln(x^2 + 1) using first principles at x = 1.
A. 1/2
B. 0
C. 1
D. 2
Show Answer & Explanation
Correct Answer: C
The calculation using first principles gives a derivative of 1 at x = 1.

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Differentiation — JEE Mathematics Practice Questions Online

This page contains 1600 practice MCQs for the chapter Differentiation in JEE Mathematics. The questions are organized by difficulty — 333 easy, 658 medium, 609 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit. This chapter covers 7 topics, giving you comprehensive coverage of the entire chapter.