Vidaara.orgClass 11 · Mathematics
CodeVID-M11-12-DER-01
Derivatives — First Principles & Rules — Assignment
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- All questions are compulsory.
- Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
- Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions
5 × 1 = 5 marks
1.
$\dfrac{d}{dx}(x^n)=$
- A.$x^{n-1}$
- B.$nx^{n-1}$
- C.$nx^n$
- D.$n$
2.
$\dfrac{d}{dx}(\sin x)=$
- A.$\cos x$
- B.$-\sin x$
- C.$\sec^2x$
- D.$-\cos x$
3.
$\dfrac{d}{dx}(c)=$
- A.$c$
- B.$0$
- C.$1$
- D.$x$
4.
$\dfrac{d}{dx}(e^x)=$
- A.$xe^{x-1}$
- B.$e^x$
- C.$\tfrac{e^x}{x}$
- D.$1$
5.
The derivative of $f$ at $x$ is $\displaystyle\lim_{h\to0}$ of:
- A.$\dfrac{f(x+h)-f(x)}{h}$
- B.$f(x+h)-f(x)$
- C.$\dfrac{f(x)}{h}$
- D.$f(x)h$
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Differentiate $x^3$.
7.
Differentiate $5x^2$.
8.
Differentiate $\cos x$.
9.
Differentiate $x$.
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
Differentiate $x^2$ from first principles.
11.
Differentiate $3x^2+2x$.
12.
Differentiate $x\sin x$.
13.
Differentiate $\dfrac{x^2+1}{x}$.
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
Find the derivative of $f(x)=\sqrt{x}$ from first principles.
15.
Differentiate $y=\dfrac{2x+1}{x-1}$ using the quotient rule.
Answer Key
Section A — Multiple Choice Questions
- (B) $nx^{n-1}$
- (A) $\cos x$
- (B) $0$
- (B) $e^x$
- (A) $\dfrac{f(x+h)-f(x)}{h}$
Section B — Short Answer (2 marks)
- $3x^2$.
- $10x$.
- $-\sin x$.
- $1$.
Section C — Short Answer (3 marks)
- $2x$.
- $6x+2$.
- $\sin x+x\cos x$.
- $1-\dfrac{1}{x^2}$.
Section D — Long Answer (5 marks)
- $\dfrac{1}{2\sqrt{x}}$.
- $\dfrac{-3}{(x-1)^2}$.
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