$\frac{d}{d x}\left(\log _a x\right)$ is equal to :
- ✓$\frac{1}{x \cdot \log _e a}$
- B$\frac{\log _e a}{x}$
- C$\frac{1}{x}$
- D$\frac{x}{\log _e a}$
Answer: A.
View full solution →76 questions across 7 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.
M.C.Q (1 Marks)
25 Q→02True False[1 Marks ]
10 Q→03Fill In The Blanks[1 Marks ]
10 Q→041 Marks Question
13 Q→052 Marks Questions
14 Q→063 Marks Question
2 Q→07Match the following.
2 Q→One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Answer: A.
View full solution →Answer: B.
View full solution →Answer: D.
View full solution →Answer: A.
View full solution →Answer: A.
View full solution →| Part (A) | Part (B) |
| 1. $\frac{d}{d x}(\sin \sqrt{x})$ | (a) $\frac{e^{\sqrt{2 x}}}{\sqrt{2 x}}$ |
| 2. $\frac{d}{d x}(x+2)^3$ | (b) $\frac{\sec ^2 \sqrt{x}}{2 \sqrt{x}}$ |
| 3. $\frac{d}{d x}\left(\frac{1}{\sqrt{x}}\right)$ | (c) $3(x+2)^2$ |
| 4. $\frac{d}{d x} e^{\sqrt{2 x}}$ | (d) $\frac{\cos \sqrt{x}}{2 \sqrt{x}}$ |
| 5. $\frac{d}{d x} \tan \sqrt{x}$ | (e) $-\frac{1}{2} x^{-3 / 2}$ |
| Part (A) | Part (B) |
| 1. $\frac{d}{d x}\left(\log _e x\right)$ | (a) $-\frac{2}{x^3}$ |
| 2. $\frac{d}{d x}\left(\log _a x\right)$ | (b) $(x+1) e^x$ |
| 3. $\frac{d}{d x}\left(\frac{1}{x^2}\right)$ | (c) $\frac{1}{x}$ |
| 4. $\frac{d}{d x} \sqrt{a x+b}$ | (d) $\frac{a}{2 \sqrt{a x+b}}$ |
| 5. $\frac{d}{d x}\left(x e^x\right)$ | (e) $\frac{1}{x \log _e a}$ |
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