Thread: function of a function differentiation!

1. function of a function differentiation!

Hi, pls trying to solve the differentiation problem below, what best method can one use to solve it.

$\displaystyle (1+x^2)^a + bx + cx^2$

thanks.

Moderator edit: [tex] tags not [tex] tags are required when using latex.

2. Re: function of a function differentiation!

Originally Posted by lawochekel
Hi, pls trying to solve the differentiation problem below, what best method can one use to solve it.

$\displaystyle (1+x^2)^a+bx+cx^2$

thanks.
$\displaystyle (1+x^2)^a + bx + cx^2$

you need to know the chain rule
what do you know about differentiation ??

3. Re: function of a function differentiation!

Originally Posted by lawochekel
Hi, pls trying to solve the differentiation problem below, what best method can one use to solve it.

$\displaystyle (1-x^2)^a+bx+cx^2$

thanks.
I am assuming a,b and c are constants.

To make this easier you can differentiate each of the terms separately: $\displaystyle \dfrac{d}{dx}((1-x^2)^a+bx+cx^2) = \dfrac{d}{dx}(1-x^2)^a + \dfrac{d}{dx} bx + \dfrac{d}{dx} cx^2$

For the second and third terms you can use the power rule $\displaystyle \left(\dfrac{d}{dx} ax^n = anx^{n-1}\right)$.

For the first term you need to use the chain rule.
Let $\displaystyle u = 1-x^2$ then $\displaystyle \dfrac{d}{dx}(1-x^2)^a = \dfrac{d}{du} \cdot \dfrac{du}{dx}$

In your case $\displaystyle \dfrac{d}{dx}(1-x^2)^a = \dfrac{d}{du} u^a \cdot \dfrac{du}{dx}$.

I'll leave you to figure the rest out, if you get stuck please post what you've tried