1
MHT CET 2023 10th May Morning Shift
+2
-0

If $$y=\cos ^{-1}\left(\frac{\mathrm{a}^2}{\sqrt{x^4+\mathrm{a}^4}}\right)$$, then $$\frac{\mathrm{d} y}{\mathrm{~d} x}$$ is

A
$$\frac{2 a^2 x}{x^4+a^4}$$
B
$$\frac{2 a^2 x^2}{\sqrt{x^4+a^4}}$$
C
$$\frac{a^4 x^4}{x^4+a^4}$$
D
$$\frac{a^4 x^2}{2 \sqrt{x^4+a^4}}$$
2
MHT CET 2023 10th May Morning Shift
+2
-0

For $$x>1$$, if $$(2 x)^{2 y}=4 \mathrm{e}^{2 x-2 y}$$, then $$(1+\log 2 x)^2 \frac{\mathrm{d} y}{\mathrm{~d} x}$$ is equal to

A
$$\frac{x \log 2 x+\log 2}{x}$$
B
$$\frac{x \log 2 x-\log 2}{x}$$
C
$$x \log 2 x$$
D
$$\log 2 x$$
3
MHT CET 2023 10th May Morning Shift
+2
-0

If $$\mathrm{f}(x)=\mathrm{e}^x, \mathrm{~g}(x)=\sin ^{-1} x$$ and $$\mathrm{h}(x)=\mathrm{f}(\mathrm{g}(x))$$, then $$\frac{\mathrm{h}^{\prime}(x)}{\mathrm{h}(x)}$$ is

A
$$\mathrm{e}^{\sin ^{-1} x}$$
B
$$\frac{1}{\sqrt{1-x^2}}$$
C
$$\sin ^{-1} x$$
D
$$\frac{\mathrm{e}^{\sin ^{-1} x}}{\sqrt{1-x^2}}$$
4
MHT CET 2023 9th May Evening Shift
+2
-0

If $$y$$ is a function of $$x$$ and $$\log (x+y)=2 x y$$, then the value of $$y^{\prime}(0)$$ is

A
1
B
$$-$$1
C
2
D
0
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