Thread: Derivatives of Logarithmic functions

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

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) ...

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

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

$\displaystyle y' = \dfrac{\sqrt{x^2+a^2} + x}{(x + \sqrt{x^2+a^2})\sqrt{x^2+a^2}}
$

see what happens now?

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??

$\displaystyle y' = \dfrac{\sqrt{x^2+a^2} + x}{(x + \sqrt{x^2+a^2})\sqrt{x^2+a^2}}
$

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

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

thanks a lot I was blind...lol