Exercise
$\frac{d^4}{dx^4}\left(\ln\left(x^2+1\right)\right)$
Step-by-step Solution
Intermediate steps
1
Find the ($1$) derivative
$\frac{2x}{x^2+1}$
Intermediate steps
2
Find the ($2$) derivative
$\frac{-2x^2+2}{\left(x^2+1\right)^2}$
Intermediate steps
3
Find the ($3$) derivative
$\frac{-4x\left(x^2+1\right)^2-4\left(-2x^2+2\right)\left(x^2+1\right)x}{\left(x^2+1\right)^{4}}$
Intermediate steps
4
Find the ($4$) derivative
$\frac{\left(-4\left(\left(x^2+1\right)^2+4x^2\left(x^2+1\right)\right)-4\left(-4x^2\left(x^2+1\right)+\left(-2x^2+2\right)\left(2x^2+x^2+1\right)\right)\right)\left(x^2+1\right)^{4}-8\left(-4x\left(x^2+1\right)^2-4\left(-2x^2+2\right)\left(x^2+1\right)x\right)\left(x^2+1\right)^{3}x}{\left(x^2+1\right)^{8}}$
Final answer to the exercise
$\frac{\left(-4\left(\left(x^2+1\right)^2+4x^2\left(x^2+1\right)\right)-4\left(-4x^2\left(x^2+1\right)+\left(-2x^2+2\right)\left(2x^2+x^2+1\right)\right)\right)\left(x^2+1\right)^{4}-8\left(-4x\left(x^2+1\right)^2-4\left(-2x^2+2\right)\left(x^2+1\right)x\right)\left(x^2+1\right)^{3}x}{\left(x^2+1\right)^{8}}$