#### Differential Calculus - Differentiability and Methods of Differentiation Two Marks Questions

11th Standard

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Maths

Time : 00:45:00 Hrs
Total Marks : 20
10 x 2 = 20
1. Differentiate the following with respect to x :$y=(x-{1\over x})^2$

2. Differentiate the following with respect to x: y=xex log x

3. Find the derivatives of the following functions with respect to corresponding independent variables:y = sin x + cos x

4. Differentiate the following:y = cos (tanx)

5. Differentiate the following: f(t)$=3\sqrt{1+tan \ t}$

6. Find ${dy\over dx}$ if x=at2 ; y=2at, t$\neq 0.$

7. Find the derivatives of the following $\sqrt{xy}=e^{(x-y)}$

8. Find $\frac { dy }{ dx } if\quad { x }^{ 4 }+{ x }^{ 2 }{ y }^{ 2 }+{ y }^{ 4 }=50.$

9. Differentiate $\sqrt { { e }^{ \sqrt { x } } } ,x>0.$

10. Differentiate x2 (x + 1)3 (x + 2)4 with respect to' 'x'.