1
MHT CET 2023 9th May Morning Shift
+2
-0

The derivative of $$\mathrm{f}(\sec x)$$ with respect to $$g(\tan x)$$ at $$x=\frac{\pi}{4}$$, where $$f^{\prime}(\sqrt{2})=4$$ and $$g^{\prime}(1)=2$$, is

A
2
B
$$\frac{1}{\sqrt{2}}$$
C
$$\sqrt{2}$$
D
$$\frac{1}{2 \sqrt{2}}$$
2
MHT CET 2022 11th August Evening Shift
+2
-0

If $$y=\log \sqrt{\frac{1+\sin x}{1-\sin x}}$$, then $$\frac{\mathrm{d} y}{\mathrm{~d} x}$$ at $$x=\frac{\pi}{3}$$ is

A
$$\frac{1}{2}$$
B
$$-\frac{1}{2}$$
C
$$2$$
D
$$\frac{1}{4}$$
3
MHT CET 2022 11th August Evening Shift
+2
-0

If $$y=\sin \left(2 \tan ^{-1} \sqrt{\frac{1+x}{1-x}}\right)$$ then $$\frac{\mathrm{d} y}{\mathrm{~d} x}$$ is equal to

A
$$\frac{-x}{\sqrt{1-x^2}}$$
B
$$\frac{-2 x}{\sqrt{1-x^2}}$$
C
$$\frac{-1}{\sqrt{1-x^2}}$$
D
$$\frac{1}{\sqrt{1-x^2}}$$
4
MHT CET 2022 11th August Evening Shift
+2
-0

If $$y^{\frac{1}{m}}+y^{\frac{-1}{m}}=2 x, x \neq 1$$, then $$\left(x^2-1\right)\left(\frac{\mathrm{d} y}{\mathrm{~d} x}\right)^2$$ is equal to

A
$$m y^2$$
B
$$m^2 y$$
C
$$m^2 y^2$$
D
$$\frac{m y^2}{2}$$
EXAM MAP
Medical
NEET