function of a function differentiation!

**lawochekel** · December 12th 2011, 01:47 AM

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

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

thanks.

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

**Amer** · December 12th 2011, 02:10 AM

Originally Posted by lawochekel

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

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

thanks.

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

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

**e^(i*pi)** · December 12th 2011, 02:58 AM

Originally Posted by lawochekel

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

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

thanks.

I am assuming a,b and c are constants.

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

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

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

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

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

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