Differentiation - Uttarakhand Board (UBSE) STD 12 Science Maths Questions

Q 1M.C.Q (1 Marks)1 Mark

$\frac{\text{d}}{\text{dx}}\Big\{\tan^{-1}\Big(\frac{\cos\text{x}}{1+\sin\text{x}}\Big)\Big\}$ equals:

A
$\frac{1}{2}$
✓
$-\frac{1}{2}$
C
$1$
D
$-1$

Answer: B.

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Q 2M.C.Q (1 Marks)1 Mark

Differential coefficient of $\sec(\tan^{-1}\text{x})$ is:

A
$\frac{\text{x}}{1+\text{x}^2}$
B
$\text{x}\sqrt{1+\text{x}^2}$
C
$\frac{\text{x}}{\sqrt{1+\text{x}^2}}$
✓
$\frac{\text{x}}{\sqrt{1+\text{x}^2}}$

Answer: D.

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Q 3M.C.Q (1 Marks)1 Mark

Let $\text{U}=\sin^{-1}\Big(\frac{2\text{x}}{1+\text{x}^2}\Big)$ and $\text{V}=\tan^{-1}\Big(\frac{2\text{x}}{1-\text{x}^2}\Big),$ then $\frac{\text{dU}}{\text{dV}}=$

A
$\frac{1}{2}$
B
$\text{x}$
C
$\frac{1-\text{x}^2}{\text{x}^2-4}$
✓
$1$

Answer: D.

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Q 4M.C.Q (1 Marks)1 Mark

If $\text{f}(\text{x})=\tan^{-1}\sqrt{\frac{1+\sin\text{x}}{1-\sin\text{x}}},0\leq\text{x}\leq\frac{\pi}{2},$ then $\text{f}'\Big(\frac{\pi}{6}\Big)$ is:

A
$-\frac{1}{4}$
B
$-\frac{1}{2}$
C
$\frac{1}{4}$
✓
$\frac{1}{2}$

Answer: D.

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Q 5M.C.Q (1 Marks)1 Mark

The derivative of $\cos^{-1}(2\text{x}^2-1)$ with respect to $\cos^{-1}\text{x}$ is:

✓
$2$
B
$\frac{1}{2\sqrt{1+\text{x}^2}}$
C
$\frac{2}{\text{x}}$
D
$1-\text{x}^2$

Answer: A.

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Q 62 Marks Questions2 Marks

If f'(1) = 2 and $\text{y}=\text{f}(\log_\text{e}\text{x}),$ find $\frac{\text{d}}{\text{dx}}\text{at x}=\text{e}.$

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Q 72 Marks Questions2 Marks

Find $\frac{\text{dy}}{\text{dx}},$ when
$\text{x}=\text{b}\sin^2\theta\text{ and y}=\text{a}\cos^2\theta$

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Q 82 Marks Questions2 Marks

If y = x|x|, find $\frac{\text{dy}}{\text{dx}}\text{ for x 0}<0.$

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Q 92 Marks Questions2 Marks

If $-\frac{\pi}{2}<\text{x}<0\text{ and y}=\tan^{-1}\sqrt{\frac{1-\cos2\text{x}}{1+\cos2\text{x}}},$ find $\frac{\text{dy}}{\text{dx}}.$

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Q 102 Marks Questions2 Marks

If $\text{y}=\sec^{-1}\Big(\frac{\text{x}+1}{\text{x}-1}\Big)+\sin^{-1}\Big(\frac{\text{x}-1}{\text{x}+1}\Big),$ then write the value of $\frac{\text{dy}}{\text{dx}}.$

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Q 113 Marks Question3 Marks

If $\text{y}=\sqrt{\cos\text{x}+\sqrt{\cos\text{x}+\sqrt{\cos\text{x}+\ .... \text{to }\infty}}},$ prove that $\frac{\text{dy}}{\text{dx}}=\frac{\sin\text{x}}{1-2\text{y}}$

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Q 123 Marks Question3 Marks

Find $\frac{\text{dy}}{\text{dx}}$ in the following cases:
$\frac{\text{x}^2}{\text{a}^2}+\frac{\text{y}^2}{\text{b}^2}=1$

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Q 133 Marks Question3 Marks

Differentiate the following functions with respect to x:
$3^{\text{x}^2+2\text{x}}$

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Q 143 Marks Question3 Marks

If f(x) is an even function, then write whether f'(x) is even of odd.

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Q 153 Marks Question3 Marks

If $\text{y}=\text{x}\sin\text{y},$ prove that $\frac{\text{dx}}{\text{dx}}=\frac{\sin^2\text{y}}{(1-\text{x}\cos\text{y})}$

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Q 165 Marks Questions5 Marks

Differentiate the following functions with respect to x:
$\text{x}^{(\sin\text{x}-\cos\text{x})}+\frac{\text{x}^2-1}{\text{x}^2+1}$

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Q 175 Marks Questions5 Marks

Differentiate $\sin^{-1}\Big(2\text{ax}\sqrt{1-\text{a}^2\text{x}^2}\Big)$ with respect to $\sqrt{1-\text{a}^2\text{x}^2},$ if $-\frac{1}{\sqrt{2}}<\text{ax}<\frac{1}{\sqrt{2}}$.

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Q 185 Marks Questions5 Marks

Differentiate the following functions from first principles:
$\text{e}^{\sqrt{2\text{x}}}$

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Q 195 Marks Questions5 Marks

Differentiate the following functions from first principles:
$\text{e}^{\sqrt{\cot\text{x}}}$

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Q 205 Marks Questions5 Marks

If $\text{y}=\frac{\text{e}^\text{x}-\text{e}^{-\text{x}}}{\text{e}^{\text{x}}+\text{e}^{-\text{x}}},$ prove that $\frac{\text{dy}}{\text{dx}}=1-\text{y}^2$

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Differentiation question types

Differentiation questions

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Differentiation Maths - Differentiation

Differentiation question types

Differentiation questions

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