#### 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 (tan x)

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

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'.