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Mathematics · 2024 · 3 marks
CBSE 2024 · Region 4 · Set 3 · Q26
Find dy/dx, if y =( cos x)^x+ cos^-1 √ x is given.
Find $\displaystyle \frac{\mathrm{dy}}{\mathrm{dx}}$, if $\displaystyle \mathrm{y}=(\cos x)^{x}+\cos ^{-1} \sqrt{x}$ is given.
Marking-scheme solution
Let $\displaystyle \mathrm{u}=(\cos x)^{x} \Rightarrow \frac{d \mathrm{u}}{d x}=(\cos x)^{x}(-x \tan x+\log (\cos x))$,
$$\mathrm{v}=\cos ^{-1} \sqrt{x} \Rightarrow \frac{d \mathrm{v}}{d x}=\frac{-1}{2 \sqrt{x-x^{2}}}
$$
Since, $\displaystyle \mathrm{y}=\mathrm{u}+\mathrm{v} \Rightarrow \frac{d \mathrm{y}}{d x}=\frac{d \mathrm{u}}{d x}+\frac{d \mathrm{v}}{d x}=(\cos x)^{x}(-x \tan x+\log (\cos x))+\frac{-1}{2 \sqrt{x-x^{2}}}$
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CBSE Class 12 Mathematics past-paper question from the 2024 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.