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Easy Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite and implicit functions MCQs for JEE

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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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