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.
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.
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