If y = x², prove that \(\frac { d^{ 2 }y }{ dx^{ 2 } } \frac { 1 }{ y } \left( \frac { dy }{ dx } \right) ^{ 2 }-\frac { y }{ x } =0\)

4

(a)

If x^myⁿ = (x + y)^m+n, prove that \(\frac { dy }{ dx } =\frac { y }{ x } \) 

4

(a)

Differentiate log \(\left( x+\sqrt { 1+{ x }^{ 2 } } \right) \)

4

(a)

Differentiate \(\frac { \sqrt { a+x } +\sqrt { a-x } }{ \sqrt { a+x } -\sqrt { a-x } } \)

4

(a)

Find \(\frac { dy }{ dx } \) for sin (xy) + \(\frac { x }{ y } \) = x² - y

4

(a)

If 2x + 2y = 2x+y, show that \(\frac { dy }{ dx } \) -2^y-x

4

(a)

Differentiare tan^-1 \(\left( \frac { acosx-bsinx }{ bcosx+asinx } \right) \)

4

(a)

Differentiate x^x +x^a + a^x + a^a 

4

(a)

Differentiate \(\left( x+\frac { 1 }{ x } \right) ^{ x }+x^{ \left( x+\frac { 1 }{ x } \right) }\)

4

(a)