Deriving a Complex Function: What is the Best Method?

[Spectre32]

Ok i have an easy function:

1/(5x^7sqrt(x)) Now i am asked to derive this. What would be the best method. I thought about the quotent rule, and I'm thinkin that's my best bet. Also, does anyone know if there is a program out there that shows steps to Derivaties and Intergration. I have my final comming up and i want to know if I'm doing all of my review problems correctly.

 

[cookiemonster]

Do you mean

\frac{1}{5x^7\sqrt{x}}

If so, this can be written as

\frac{1}{5}x^{-15/2}

and differentiated using the power rule.

cookiemonster

 

[Spectre32]

ahhh whoops, i forgot about that, Thanks for the help.

 

[Gokul43201]

Your description of the function is not clear. Is the sqrt(x) also in the exponent ?

If you mean y = 1/[5*x^{7*sqrt(x)}], it's a little harder. Then you take the logarithm on both sides - which converts the exponent into a product - before differentiating.

That way, the answer would be y' = [-7/{sqrt(x)*x^(7*sqrt(x))}]*[1 - (1/2)*log(x)]