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**Continuity & Differentiability **

**Question 1: Differentiate the following w.r.t. x: **

**Answer**

Let y =

By using the quotient rule, we obtain

**Question 2: Differentiate the following w.r.t. x: e ^{sin-1x}**

**Answer**

Let y = **e ^{sin-1x}**

By using the chain rule, we obtain

**Question 3: Differentiate the following w.r.t. x:**

**Answer**

Let y =

By using the chain rule, we obtain

**Question 4: Differentiate the following w.r.t. x: sin(tan ^{-1}e^{-x})**

**Answer**

Let y = sin(tan^{-1}e^{-x})

By using the chain rule, we obtain

**Question 5: Differentiate the following w.r.t. x: ****log(cose ^{x})**

**Answer**

Let y = log(cose^{x})

By using the chain rule, we obtain

**Question 6: Differentiate the following w.r.t. x:**

**Answer**

**Question 7: Differentiate the following w.r.t. x: **

**Answer**

Let

**Question 8: Differentiate the following w.r.t. x:**

**Answer**

Let y =

By using the chain rule, we obtain

**Question 9: Differentiate the following w.r.t. x:**

**Answer**

Let y =

By using the quotient rule, we obtain

**Question 10: Differentiate the following w.r.t. x:** **, x>0**

**Answer**

Let y =

By using the chain rule, we obtain

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