Differentiation - Rajasthan Board (RBSE) 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:

$\frac{1}{2}$
$-\frac{1}{2}$
$1$
$-1$

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

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

$\frac{\text{x}}{1+\text{x}^2}$
$\text{x}\sqrt{1+\text{x}^2}$
$\frac{\text{x}}{\sqrt{1+\text{x}^2}}$
$\frac{\text{x}}{\sqrt{1+\text{x}^2}}$

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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 $\frac{\text{dU}}{\text{dV}}=$

$\frac{1}{2}$
$\text{x}$
$\frac{1-\text{x}^2}{\text{x}^2-4}$
$1$

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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:

$-\frac{1}{4}$
$-\frac{1}{2}$
$\frac{1}{4}$
$\frac{1}{2}$

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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:

$2$
$\frac{1}{2\sqrt{1+\text{x}^2}}$
$\frac{2}{\text{x}}$
$1-\text{x}^2$

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Q 62 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 72 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 82 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 92 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 102 Marks Questions2 Marks

Differentiate $x^2$ with respect to $x^3.$

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Q 113 Marks Question3 Marks

Find $\frac{\text{dy}}{\text{dx}}$ in the following cases:
$\tan^{-1}\big(\text{x}^2+\text{y}^2\big)=\text{a}$

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Q 123 Marks Question3 Marks

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

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Q 133 Marks Question3 Marks

If $\text{x}=3\sin\text{t}-\sin3\text{t},\text{y}=3\cos3\text{t}-\cos3\text{t}$ find $\frac{\text{dy}}{\text{dx}}\text{ at t}=\frac{\pi}{3}$

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Q 143 Marks Question3 Marks

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

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Q 153 Marks Question3 Marks

Differentiate:$\tan(\text{x}^\circ+45^\circ)$

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Q 165 Marks Questions5 Marks

Find $\frac{\text{dy}}{\text{dx}}$ in the following cases: $y^3 - 3xy^2 = x^3 + 3x^2y$

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Q 175 Marks Questions5 Marks

If $x^{16}y^9 = (x + y)^{17},$ prove that $\text{x}\frac{\text{dy}}{\text{dx}}=2\text{y}$

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Q 185 Marks Questions5 Marks

Differentiate the following functions with respect to x:
$(\log\text{x})^{\cos\text{x}}$

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Q 195 Marks Questions5 Marks

If $e^x + x^y = e^{x+y},$ prove that $\frac{\text{dy}}{\text{dx}}+\text{e}^{\text{y}-\text{x}}=0$

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Q 205 Marks Questions5 Marks

Differentiate $\tan^{-1}\Big(\frac{\text{x}-1}{\text{x}+1}\Big)$ with respect to $\sin^{-1}\big(3\text{x}-4\text{x}^3\big),$ if $-\frac{1}{2}<\text{x}<\frac{1}{2}$

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Differentiation MATHS - Differentiation

Differentiation question types

Differentiation questions

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