Derivatives of Logarithmic functions

**Aniff** · February 13th 2011, 07:47 AM

can someone help me to find the derivative of this function??

y=ln(x+(x^2+a^2)^1/2)

I'm not getting the answer 1/(x^2+a^2) from my textbook

thanks

**skeeter** · February 13th 2011, 08:01 AM

Originally Posted by Aniff

can someone help me to find the derivative of this function??

y=ln(x+(x^2+a^2)^1/2)

I'm not getting the answer 1/(x^2+a^2) from my textbook

thanks

your textbook "answer" is incorrect (unless you forgot an exponent or radical in the denominator) ...

$y' = \dfrac{1 + \dfrac{x}{\sqrt{x^2+a^2}}}{x + \sqrt{x^2+a^2}}$

multiply numerator and denominator by $\sqrt{x^2+a^2}$ to clear the inner fraction in the numerator ...

$y' = \dfrac{\sqrt{x^2+a^2} + x}{(x + \sqrt{x^2+a^2})\sqrt{x^2+a^2}}<br />$

see what happens now?

**Aniff** · February 13th 2011, 08:11 AM

yeah sorry i missed the sqrt...should be 1/(x^2+a^2)^1/2

ok I already got to that point but could not simplify any further??

**skeeter** · February 13th 2011, 08:14 AM

$y' = \dfrac{\sqrt{x^2+a^2} + x}{(x + \sqrt{x^2+a^2})\sqrt{x^2+a^2}}<br />$

LOOK again at the factors in the numerator and denominator ...

**Aniff** · February 13th 2011, 08:18 AM

ooohh okay I can see it now...I can cancel the common factors

thanks a lot I was blind...lol

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