Second Derivative (Chain rule ?)

[R5232]

I am supposed to find the first and second derivative of (x[sup:2xx6g0hf]2[/sup:2xx6g0hf]+2)[sup:2xx6g0hf]5[/sup:2xx6g0hf]

The first derivative follows:

5(x[sup:2xx6g0hf]2[/sup:2xx6g0hf]+2)[sup:2xx6g0hf]4[/sup:2xx6g0hf] (2x)
10x(x[sup:2xx6g0hf]2[/sup:2xx6g0hf]+2)[sup:2xx6g0hf]4[/sup:2xx6g0hf]

Now, Working on the second derivative, I think I run into trouble.

(10x)(x[sup:2xx6g0hf]2[/sup:2xx6g0hf]+2)[sup:2xx6g0hf]4[/sup:2xx6g0hf]
(d/dx (10x) * (x[sup:2xx6g0hf]2[/sup:2xx6g0hf]+2)[sup:2xx6g0hf]4[/sup:2xx6g0hf]) + ((10x) * (d/dx (x[sup:2xx6g0hf]2[/sup:2xx6g0hf]+2)[sup:2xx6g0hf]4[/sup:2xx6g0hf]
((10) * (x[sup:2xx6g0hf]2[/sup:2xx6g0hf]+2)[sup:2xx6g0hf]4[/sup:2xx6g0hf]) + ((10x) * (8x(x[sup:2xx6g0hf]2[/sup:2xx6g0hf]+2)[sup:2xx6g0hf]3[/sup:2xx6g0hf]

Beyond that, I think I mess something up. I think I should multiply everything out, but it doesn't end up to be the correct answer in the book

Thanks in advance!

 

[pka]

Your calculus is just fine.
Now do the algebra.
Factor and multiply out.

 

[R5232]

(10x)(x2+2)[sup:18xd45lk]4[/sup:18xd45lk]
(d/dx (10x) * (x[sup:18xd45lk]2[/sup:18xd45lk]+2)[sup:18xd45lk]4[/sup:18xd45lk]) + ((10x) * (d/dx (x[sup:18xd45lk]2[/sup:18xd45lk]+2)[sup:18xd45lk]4[/sup:18xd45lk]
((10) * (x[sup:18xd45lk]2[/sup:18xd45lk]+2)[sup:18xd45lk]4[/sup:18xd45lk]) + ((10x) * (8x(x[sup:18xd45lk]2[/sup:18xd45lk]+2)[sup:18xd45lk]3[/sup:18xd45lk]
--
((10 * (x[sup:18xd45lk]8[/sup:18xd45lk]+16)) + ((10x) * (8x(x[sup:18xd45lk]6[/sup:18xd45lk]+8)
(10x[sup:18xd45lk]8[/sup:18xd45lk]+160) + (80x[sup:18xd45lk]8[/sup:18xd45lk]+64x[sup:18xd45lk]2[/sup:18xd45lk])
90x[sup:18xd45lk]8[/sup:18xd45lk]+64x[sup:18xd45lk]2[/sup:18xd45lk]+160

Thats what I figured the answer out to be. I may have looked over a factorisable part of the problem though.

 

[pka]

\(\displaystyle 10\left( {x^2 + 2} \right)^4 + \left( {10x} \right)\left[ {8x\left( {x^2 + 2} \right)^3 } \right] = 10\left( {x^2 + 2} \right)^3 \left[ {\left( {x^2 + 2} \right) + \left( x \right)\left( {8x} \right)} \right]\)

RECALL YOUR ALGEBRA. It will save your life in calculus.

 

[Deleted member 4993]

(10x)(x2+2)[sup:2pgf9wif]4[/sup:2pgf9wif]
(d/dx (10x) * (x[sup:2pgf9wif]2[/sup:2pgf9wif]+2)[sup:2pgf9wif]4[/sup:2pgf9wif]) + ((10x) * (d/dx (x[sup:2pgf9wif]2[/sup:2pgf9wif]+2)[sup:2pgf9wif]4[/sup:2pgf9wif]
((10) * (x[sup:2pgf9wif]2[/sup:2pgf9wif]+2)[sup:2pgf9wif]4[/sup:2pgf9wif]) + ((10x) * (8x(x[sup:2pgf9wif]2[/sup:2pgf9wif]+2)[sup:2pgf9wif]3[/sup:2pgf9wif]
--
((10 * (x[sup:2pgf9wif]8[/sup:2pgf9wif]+16)) + ((10x) * (8x(x[sup:2pgf9wif]6[/sup:2pgf9wif]+8) <<<< These are incorrect

(10x[sup:2pgf9wif]8[/sup:2pgf9wif]+160) + (80x[sup:2pgf9wif]8[/sup:2pgf9wif]+64x[sup:2pgf9wif]2[/sup:2pgf9wif])
90x[sup:2pgf9wif]8[/sup:2pgf9wif]+64x[sup:2pgf9wif]2[/sup:2pgf9wif]+160

Thats what I figured the answer out to be. I may have looked over a factorisable part of the problem though.

((10) * (x[sup:2pgf9wif]2[/sup:2pgf9wif]+2)[sup:2pgf9wif]4[/sup:2pgf9wif]) + ((10x) * (8x(x[sup:2pgf9wif]2[/sup:2pgf9wif]+2)[sup:2pgf9wif]3[/sup:2pgf9wif]

=10*(x[sup:2pgf9wif]2[/sup:2pgf9wif]+2)[sup:2pgf9wif]3[/sup:2pgf9wif] * [(x[sup:2pgf9wif]2[/sup:2pgf9wif]+2) + 8x[sup:2pgf9wif]2[/sup:2pgf9wif]]

Now continue.....