Solve frac{30m^3x+1+46m^5x+5m^5x^2-23{m}^{5x-2}+3{m}^3x-3}{{m}^5x-3-8{m}^3x-2+6{m}^3x-1}

$$\frac{ 30 { m }^{ 3x+1 } +46 { m }^{ 5x } +5 { m }^{ 5 { x }^{ 2 } } -23 { m }^{ 5x-2 } +3 { m }^{ 3x-3 } }{ { m }^{ 5x-3 } -8 { m }^{ 3x-2 } +6 { m }^{ 3x-1 } }$$

Evaluate

$$\frac{5m^{5x^{2}}+30m^{3x+1}+3m^{3\left(x-1\right)}-23m^{5x-2}+46m^{5x}}{6m^{3x-1}+m^{5x-3}-8m^{3x-2}}$$

Differentiate w.r.t. x

$$\frac{\ln(m)\left(300xm^{x\left(5x+3\right)+5}-400xm^{x\left(5x+3\right)+4}+50xm^{5x\left(x+1\right)+3}+120m^{\left(5x-2\right)\left(x+1\right)+6}-25m^{5x\left(x+1\right)+3}-90m^{5x^{2}+3x+5}-828m^{2\left(4x+1\right)+3}+72m^{2\left(3x-1\right)+3}+115m^{5\left(2x-1\right)+6}+920m^{2\left(4x-1\right)+4}+1044m^{2\left(4x-1\right)+6}-15m^{2\left(4x-3\right)+6}-54m^{2\left(3x-2\right)+6}-115m^{2\left(5x-1\right)+3}-552m^{4\left(2x-1\right)+6}+54m^{6x+2}+1380m^{8x+5}-72m^{6x+1}-276m^{8x+3}-1840m^{8x+4}+9m^{8x}\right)}{m^{6}\left(6m^{3x-1}+m^{5x-3}-8m^{3x-2}\right)^{2}}$$