Derivatives - Gujarat Board (GSEB) STD 11 Science MATHS Questions

Q 1MCQ1 Mark

If $\text{f}(\text{x})=1-\text{x}+\text{x}^2-\text{x}^3+\dots-\text{x}^{99}+\text{x}^{100},$then f'(1) equals

A
150
B
-50
C
-150
✓
50

Answer: D.

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Q 2MCQ1 Mark

Let $\text{f}(\text{x})=\text{x}-[\text{x}],\text{x}\in\text{R},$ then $\text{f}'\Big(\frac{1}{2}\Big)$ is:

A
$\frac{3}{2}$
✓
1
C
0
D
-1

Answer: B.

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Q 3MCQ1 Mark

If $\text{f(x)}=\frac{\text{x}^\text{n}-\text{a}^\text{n}}{\text{x}-\text{a}},$ then $\text{f}'\text{(a)}$ is:

A
$1$
B
$0$
C
$\frac{1}{2}$
✓
$\text{dose not exist}$

Answer: D.

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Q 4MCQ1 Mark

If $\text{y}=\frac{\sin(\text{x}+9)}{\cos\text{x}},$ then $\frac{\text{dy}}{\text{dx}}$ at x = 0 is:

✓
$\cos9$
B
$\sin9$
C
$0$
D
$1$

Answer: A.

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Q 5MCQ1 Mark

if $\text{f}(\text{x})=1+\text{x}+\frac{\text{x}^2}{2}+\dots+\frac{\text{x}^{100}}{100},$then f'(1) is equal to:

A
$\frac{1}{100}$
✓
100
C
50
D
0

Answer: B.

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Q 6(Each question 1 marks)1 Mark

Write the value of $\frac{\text{d}}{\text{dx}}\big\{(\text{x}+|\text{x}|)|\text{x}|\big\}$

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Q 7(Each question 1 marks)1 Mark

If $\text{f}(\text{x})=\frac{\text{x}^2}{|\text{x}|},$ write $\frac{\text{d}}{\text{dx}}\big(\text{f}(\text{x})\big)$

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Q 8(Each question 1 marks)1 Mark

If $|\text{x}|<1$ and $\text{y}=1+\text{x}+\text{x}^2+\text{x}^3+\dots,$ then write the value of $\frac{\text{dy}}{\text{dx}}.$

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Q 9(Each question 1 marks)1 Mark

Write the value of $\frac{\text{d}}{\text{dx}}(\log|\text{x}|)$

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Q 10(Each question 1 marks)1 Mark

Write the value of $\frac{\text{d}}{\text{dx}}(\text{x}|\text{x}|)$

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Q 11(Each question 2 marks)2 Marks

Differentiate the following function with respect to $(\text{x})$:$\log_3\text{x}+3\log_\text{e}\text{x}+2\tan\text{x}$

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Q 12(Each question 2 marks)2 Marks

Differentiate the following function with respect to $\text{x}$:$\text{x}^3\text{e}^\text{x}$

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Q 13(Each question 2 marks)2 Marks

Differentiate the following functions with respect to x:$\frac{\text{e}^\text{x}}{1+\text{x}^2}$

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Q 14(Each question 2 marks)2 Marks

Differentiate the following function with respect to $(\text{x})$:$\frac{1}{\sin\text{x}}+2^{\text{x}+3}+\frac{4}{\log\text{x}^3}$

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Q 15(Each question 2 marks)2 Marks

Differentiate the following function with respect to $(\text{x})$:$2\sec\text{x}+3\cot\text{x}-4\tan\text{x}$

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Q 16(Each question 3 marks)3 Marks

Differentiate the following function with respect to x:$(\text{ax}+\text{b})^\text{n}(\text{cx}+\text{d})^\text{m}$

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Q 17(Each question 3 marks)3 Marks

Differentiate the following from first principle:$\text{e}^{\text{3x}}$

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Q 18(Each question 3 marks)3 Marks

Find the slope of the tangent to the curve $\text{f}(\text{x})=\text{2x}^6+\text{x}^4-1$ at$\text{x}=1$

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Q 19(Each question 3 marks)3 Marks

Differentiate the following from first principle:$\text{x}^3-\text{5x}^2+\text{x}-5$

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Q 20(Each question 3 marks)3 Marks

Differentiate the following function with respect to $(\text{x})$:$\cos(\text{x}+\text{h})$

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Q 21(Each question 4 marks)4 Marks

Differentiate the following from first principle$\sin\sqrt{2\text{x}}$

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Q 22(Each question 4 marks)4 Marks

Differentiate the following from first principle$3^{\text{x}^2}$

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Q 23(Each question 4 marks)4 Marks

Differentiate the following from the first principle$\text{x}^2\sin\text{x}$

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Q 24(Each question 4 marks)4 Marks

Differentiate the following from the first principle$\sqrt{\sin\text{2x}}$

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Q 25(Each question 4 marks)4 Marks

For the function $\text{f}(\text{x})=\frac{\text{x}^{100}}{100}+\frac{\text{x}^{99}}{99}+\dots+\frac{\text{x}^2}{2}+\text{x}+1.$Prove that $\text{f}'(1)=100\text{f}'(0).$

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Derivatives MATHS - Derivatives

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