Solve ((2x^2+1)^2ln2x)^prime

$$( ( 2 x ^ { 2 } + 1 ) ^ { 2 \ln 2 x } ) ^ { \prime }$$

Evaluate

$$\frac{2\left(2x^{2}\ln(2x^{2}+1)+4x^{2}\ln(x)+\ln(2x^{2}+1)+4\ln(2)x^{2}\right)\left(2x^{2}+1\right)^{2\left(\ln(x)+\ln(2)\right)}}{x\left(2x^{2}+1\right)}$$

Differentiate w.r.t. x

$$\frac{2\left(2x^{2}+1\right)^{2\left(\ln(x)+\ln(2)\right)}\left(8x^{4}\ln(2x^{2}+1)^{2}+8\left(x\ln(2x^{2}+1)\right)^{2}+32x^{4}\ln(x)\ln(2x^{2}+1)+32\ln(2)x^{4}\ln(2x^{2}+1)-4x^{4}\ln(2x^{2}+1)+32x^{4}\ln(x)^{2}+16x^{2}\ln(x)\ln(2x^{2}+1)+64\ln(2)x^{4}\ln(x)-8x^{4}\ln(x)+16\ln(2)x^{2}\ln(2x^{2}+1)-4x^{2}\ln(2x^{2}+1)+2\ln(2x^{2}+1)^{2}+4x^{2}\ln(x)-\ln(2x^{2}+1)+32\ln(2)^{2}x^{4}-8\ln(2)x^{4}+16x^{4}+4\ln(2)x^{2}+8x^{2}\right)}{\left(x\left(2x^{2}+1\right)\right)^{2}}$$