Differentiation - Gujarat Board (GSEB) 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:

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

View full solution →

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

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

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

View full solution →

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

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

View full solution →

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:

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

View full solution →

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:

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

View full solution →

Q 62 Marks2 Marks

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

View full solution →

Q 72 Marks2 Marks

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

View full solution →

Q 82 Marks2 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 $\frac{\text{dy}}{\text{dx}}.$

View full solution →

Q 92 Marks2 Marks

Differentiate x² with respect to x³.

View full solution →

Q 102 Marks2 Marks

If $\text{f}'\text{(x)}=\sqrt{2\text{x}^2-1}$ and $\text{y}=\text{f}(\text{x}^2),$ then find $\frac{\text{dy}}{\text{dx}}\text{at x}=1.$

View full solution →

Q 113 Marks3 Marks

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

View full solution →

Q 123 Marks3 Marks

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

View full solution →

Q 133 Marks3 Marks

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

View full solution →

Q 143 Marks3 Marks

Differentiate:

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

View full solution →

Q 153 Marks3 Marks

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

View full solution →

Q 164 Marks4 Marks

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

View full solution →

Q 174 Marks4 Marks

Differentiate the following functions with respect to x:
$\big(\sin^{-1}\text{x}^4\big)^4$

View full solution →

Q 184 Marks4 Marks

Differentiate the following functions from first principles:

e^ax+b.

View full solution →

Q 194 Marks4 Marks