CBSE 2024 · Region 5 · Set 1 · Q26 · 3 marks
Find $\displaystyle \frac{\mathrm{dy}}{\mathrm{dx}}$, if $\displaystyle (\cos \mathrm{x})^{\mathrm{y}}=(\cos \mathrm{y})^{\mathrm{x}}$.If $\displaystyle \sqrt{1-\mathrm{x}^{2}}+\sqrt{1-\mathrm{y}^{2}}=a(\mathrm{x}-\mathrm{y})$, prove that $\displaystyle \frac{d \mathrm{y}}{d \mathrm{x}}=\sqrt{\frac{1-\mathrm{y}^{2}}{1-\mathrm{x}^{2}}}$.
Find $\displaystyle \frac{\mathrm{dy}}{\mathrm{dx}}$, if $\displaystyle (\cos \mathrm{x})^{\mathrm{y}}=(\cos \mathrm{y})^{\mathrm{x}}$.
If $\displaystyle \sqrt{1-\mathrm{x}^{2}}+\sqrt{1-\mathrm{y}^{2}}=a(\mathrm{x}-\mathrm{y})$, prove that $\displaystyle \frac{d \mathrm{y}}{d \mathrm{x}}=\sqrt{\frac{1-\mathrm{y}^{2}}{1-\mathrm{x}^{2}}}$.
Marking-scheme solution
(a)
Taking 'log' on both sides of $\displaystyle (\cos \mathrm{x})^{\boldsymbol{\mathrm{y}}} \boldsymbol{=}(\cos \mathrm{y})^{\boldsymbol{\mathrm{x}}}$, we get $\displaystyle \mathrm{y} \log \cos \mathrm{x}=\mathrm{x} \log \cos \mathrm{y}$
Continuity and DifferentiabilityLogarithmic DifferentiationApplyshort_answerhard
More from Continuity and Differentiability
- If f(x)=. is continuous at x=0, then the value of a is:2025 · asked 4×
- The value of k for which function f(x)=. is differentiable at x=0 is:2023 · asked 3×
- If y=( cos x- sin x)/( cos x+ sin x), then (d y)/(d x) is:2023 · asked 3×
- If f(x)=. is continuous at x=0, then the value of k is:2025 · asked 3×
- Differentiate sec^-1( 1√1-x^2) w.r.t. sin^-1(2 x √1-x^2). OR If y= tan x+ sec x, then prove that (d^2 y)/(d…2023 · asked 3×
- If f(x)=. is continuous at x=-1, then the value of k is:2026 · asked 3×
- The value of k for which the function f(x)= casesx^2 sin 1/x, & x ≠ 0 k(x+1), & x=0 cases is a continuous…2026 · asked 3×
- If tan ((x+y)/(x-y))=k, then (dy)/(dx) is equal to2023 · asked 3×
CBSE Class 12 Mathematics past-paper question from the 2024board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.