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

If $$x^2+y^2=\mathrm{t}+\frac{1}{\mathrm{t}}$$ and $$x^4+y^4=\mathrm{t}^2+\frac{1}{\mathrm{t}^2}$$, then $$\frac{\mathrm{d} y}{\mathrm{~d} x}$$ is equal to

A
$$\frac{y}{x}$$
B
$$\frac{-y}{x}$$
C
$$\frac{x}{y}$$
D
$$\frac{-x}{y}$$
2
MHT CET 2023 9th May Morning Shift
+2
-0

If $$\mathrm{f}(1)=1, \mathrm{f}^{\prime}(1)=3$$, then the derivative of $$\mathrm{f}(\mathrm{f}(\mathrm{f}(x)))+(\mathrm{f}(x))^2$$ at $$x=1$$ is

A
12
B
19
C
23
D
33
3
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
$$\frac{1}{2 \sqrt{2}}$$
4
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
$$\frac{1}{4}$$
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