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Match the functionf(x) in Column A with its derivativef{}'(x) in Column B

\begin{array}{|l|l|l|l|} \hline \text { S.No } & \text { Column A } & \text { S.No. } & \text { Column B } \\ \hline \text { 1. } & \sin \left(x^2+1\right) & \text { A. } & \frac{1}{x} \\ \hline \text { 2. } & 2 \cos (x) & \text { B. } & 6 x^2 y\left(x^2 y^2+\ln x\right)^2 \\ \hline \text { 3. } & \ln (x) & \text { C. } & 2 x \cos \left(x^2+1\right) \\ \hline \text { 4. } & \left(x^2 y^2+\ln x\right)^3 & \text { D. } & 3\left(x^2+\sin x\right)^2(2 x+\cos x) \\ \hline \text { 5. } & \left(x^2+\sin x\right)^3 & \text { E. } & 2 \sin (x) \\ \hline \end{array}

Option: 1

1-b, 2-e, 3-a, 4-c, 5-d


Option: 2

1-b, 2-c, 3-a, 4-e, 5-d


Option: 3

1-c, 2-e, 3-a, 4-b, 5-d


Option: 4

1-d, 2-e, 3-a, 4-b, 5-c


Answers (1)

best_answer

\text { 1. } \sin \left(x^2+1\right)

\frac{d\left(\sin (x)^2+1\right)}{d x}=\frac{d(\sin (u)+1)}{d u} \cdot \frac{d(x)^2}{d x}=\cos u+1.2 x=2 x \cos \left(x^2+1\right)2. \frac{d(2 \cos (x))}{d x}=2 \sin (x)

3. \frac{d(\ln (x))}{d x}=\frac{1}{x}

4. \frac{d\left(x^2 y^2+\ln x\right)^3}{d x}=\frac{3\left(x^2 y^2+\ln x\right)^2 \cdot d\left(x^2 y^2+\ln x\right)}{d x}

\begin{aligned} & =\frac{3\left(x^2 y^2+\ln x\right)^2 \cdot\left(2 x y^2+1\right)}{x} \\ & =6 x^2 y\left(x^2 y^2+\ln x\right)^2 \end{aligned}

\text { 5. }\left(x^2+\sin x\right)^3=3\left(x^2+\sin x\right)^2 \cdot(2 x+\cos x)

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Deependra Verma

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