Question

find nth derivative of log(x^2+a^2)

Answer 1

hope it helps you..................

Answer 2

Answer:

Step-by-step explanation:

We  have to find the nth derivative of the given;

y = $log (x^{2} + a^{2} )$

We have to drivate the above equation n time to find the derivative of the given equation;

So,

$\frac{dy}{dx}  = \frac{2x}{x^{2}+y^{2}  }$

Now derivating 2nd time w.r.t x , we get

$\frac{d^{2y} }{dx^{2} } = 2 \times \frac{(a^{2} -x^{2)} }{(x^{2} + y^{2} )}$

Differentiating 3rd time w.r.t x , to observe the pattern;

$\frac{d^{3} y}{dx^{3} } = 4 \times x\frac{ (-3 a^{2} +x^{2} )}{(x^{2}+ a^{2} ) ^{3}  }$

Now, we have observe the pattern , so we can go fot the nth derivative;

$\frac{d^{n} y}{dx^{n} } = (n+1) \times x\frac{ (-na^{2} +x^{2} )}{(x^{2}+ a^{2} ) ^{3}  }$

So, we have found the nth derivative of the given question.