微積分求解~~~~~~~~?

Ans :

Sol
y=[x^3√(5x)/Sinx]^3
y=5√5 [x^(7/2)/Sinx]^3
y=5√5x^(21/2)/Sin^3 x
ySin^3 x=5√5x^(21/2)
y*3Sin^2 x*Cosx+Sin^3 xy’=5√5*(21/2)x^(19/2)
3y*Sin^3 x*Cosx/Sinx+Sin^3 xy’=5√5*(21/2)x^(19/2)
3*5√5x^(21/2)*Cosx/Sinx+Sin^3 xy’=5√5*(21/2)x^(19/2)
15√5x^(21/2)*Cotx+Sin^3 xy’=5√5*(21/2)x^(19/2)
Sin^3 xy’=5√5*(21/2)x^(19/2)－15√5x^(21/2)*Cotx
y’=5√5*(21/2)x^(19/2)/Sin^3 x－15√5x^(21/2)*Cotx/Sin^3 x
y’=5√5*(21/2)x^(19/2)/Sin^3 x－15√5x^(21/2)*Cosx/Sin^4 x