If f(x)=ln(2x), then f′(3) equals:
- 1/3
- 2/3
- 1/6
- 3/2
Show answer and explanation
Answer: A. 1/3
f′(x)=1/x; f′(3)=1/3.
FSC Mathematics: Differentiation, questions with answers
Practise 61 real Federal Board questions on Differentiation from 2023 to 2026. See the answer and explanation as soon as you answer.
61real questions
24multiple choice
5exam sessions
About Differentiation in FSC Mathematics
Differentiation is one of the 14 main chapters in our Federal Board FSC Mathematics question bank (12th class), and about 13% of its real questions come from it. Tayyari Karo has 61 real questions on this chapter from 2023 to 2026; 24 are multiple choice and marked instantly, and the rest are short and long questions with a model answer. By difficulty: 31 medium, 19 hard, 11 easy.
Work through the questions below, then open the explanation for each one. Redo the ones you missed a few days later.
Try 8 real questions
These are real past-paper questions. Think of your answer first, then open the explanation.
d/dx(eˣ+3e^(−3x)) =
- eˣ−9e^(−3x)
- eˣ+9e^(−3x)
- eˣ−6e^(−3x)
- eˣ+6e^(−3x)
Show answer and explanation
Answer: A. eˣ−9e^(−3x)
d/dx(3e^(−3x))=−9e^(−3x).
If (1/x²)dy/dx=3 then solution y(x) of differential equation is:
- x³+c
- x³/3+c
- 3x³+c
- −x³+c
Show answer and explanation
Answer: A. x³+c
dy=3x²dx ⇒ y=x³+c.
If z=x²+xy+y², then ∂z/∂x is:
- 2x+2y
- x+y
- 2x+x
- 2x+y
Show answer and explanation
Answer: D. 2x+y
Treat y as constant: ∂z/∂x=2x+y.
The degree of the differential equation (d²y/dx²)³+dy/dx=x is:
- 3
- 5
- 6
- 2
Show answer and explanation
Answer: A. 3
Power of the highest-order derivative term is 3.
If f(x)=e^(ln(Sinx)), then what is the value of f′(π/2)?
- −1
- 0
- −1
- −3
Show answer and explanation
Answer: B. 0
e^(ln(Sinx)) = Sinx, so f′(x)=Cosx, and f′(π/2)=Cos(π/2)=0.
The population of a city grows at a rate proportional to its current population. In 2020, the population was 50,000. In 2025, it became 60,000. (a) Find the growth constant k. (b) Predict the population in 2030.
Show model answer
P=P₀e^(kt); 60000=50000e^(5k) ⇒ e^(5k)=1.2 ⇒ k=(1/5)ln(1.2)
k ≈ 0.0365 per year
At t=10 (year 2030): P=50000e^(10k)=50000(1.2)²=50000(1.44)
P(2030) ≈ 72,000
Differentiate y=sin⁻¹(2x/(1+x²)) w.r.t. x.
Show model answer
Let x=tanθ: 2x/(1+x²)=sin2θ, so y=sin⁻¹(sin2θ)=2θ=2tan⁻¹x
dy/dx = 2/(1+x²)
Sessions with Differentiation questions
| Session | Questions |
|---|---|
| 2026 Annual | 13 |
| 2025 1st Annual | 17 |
| 2025 2nd Annual | 16 |
| 2024 Annual | 8 |
| 2023 Annual | 7 |
Common questions
What does the Differentiation chapter cover on this page?
61 real Federal Board (FBISE) Mathematics questions on Differentiation from 2023 to 2026, for 12th class. Each one shows the session it came from.
Are the answers official?
No. We could not find an official FBISE marking scheme for these papers, so the answers and explanations are written by Tayyari Karo for practice. Check anything important with your teacher or textbook.
Is it free?
You can start free with no signup. A small set of papers per subject is free, and Premium unlocks the full question bank.
Other Mathematics chapters
- Conic Sections 46
- Vectors 46
- Integration 39
- Functions and Limits 31
- Trigonometric Identities 30
- Matrices and Determinants 29
- Sequences and Series 28
- Introduction to Analytic Geometry 28
- Fundamentals of Trigonometry 26
- Quadratic Equations 21
- Binomial Theorem 20
- Permutation/Combination/Probability 19
- Number Systems 17