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Important Questions: Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite and implicit functions for JEE

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The most important Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite and implicit functions questions for JEE cover conceptual traps, standard results, and numerical patterns from Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite and implicit functions. Goodmarks provides 4+ high-yield MCQs with full solutions.

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Part of Limit, Continuity and Differentiability in JEE Main Mathematics.

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Q1MathsUnit 7: Limit, Continuity and Differentiability
If y=sin⁡−112(1+x+1−x)y=\sin ^{-1} \frac{1}{2}(\sqrt{1+x}+\sqrt{1-x}) then y′=y^{\prime}=
Q2MathsUnit 7: Limit, Continuity and Differentiability
Assertion STATEMENT 1: Let f(x)=\boldsymbol{f}(\boldsymbol{x})= sin⁡−1(2x1+x2),f′(2)=−25\sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right), f^{\prime}(2)=-\frac{2}{5} Reason STATEMENT 2:sin⁡−1(2x1+x2)=π2: \sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right)=\pi 2tan⁡−1x∀x>12 \tan ^{-1} x \forall x>1
Q3MathsUnit 7: Limit, Continuity and Differentiability
Ifxy=ex−y\boldsymbol{I} \boldsymbol{f} \quad \boldsymbol{x}^{\boldsymbol{y}}=\boldsymbol{e}^{\boldsymbol{x}-\boldsymbol{y}} \quad then
Q4MathsUnit 7: Limit, Continuity and Differentiability
If cos⁡−1(x2−y2x2+y2)=k\cos ^{-1}\left(\frac{x^{2}-y^{2}}{x^{2}+y^{2}}\right)=k (a constant) then dydx=\frac{d y}{d x}=

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