Question

Hallar la derivada de y = x^4(2x^3+5)^3

Answer 1

f(x)= x⁴(2x³+5)³
f₍x₎'=(4x³)(2x³+5)³+(x⁴)[3(2x³+5)²(6X²)]
f₍x₎'= (4x³)(8x⁹+60x⁵+150x³+125)+(x⁴)[(18x²)(4x⁵+20x³+25)]
     =32x¹²+240x⁸+600x⁶+500x³+x⁴(72x⁷+360x⁵+450x²)
     =32x¹²+240x⁸+600x⁶+500x³+72x¹¹+360x⁹+450x⁶
     =32x¹²+72x¹¹+360x⁹+240x⁸+1050x⁶+500x³
     =2x³(16x⁹+36x⁸+180x⁶+120x⁵+525x³+250)