Odpowiedź:
[tex]5x^{3} (6x-9)^5=5x^{3} [3(2x-3)]^5=5\cdot3^5x^3(2x-3)^5=1215x^3(2x-3)^5\\(x^{3} (2x-3)^5)'=(x^{3} )'(2x-3)^5+[(2x-3)^5]'\cdot x^{3} =\\3x^{2} (2x-3)^5+5\cdot2(2x-3)^4x^3=x^2(2x-3)^4[3(2x-3)+10x]=\\x^2(2x-3)^4(6x-9+10x)=x^2(2x-3)^4(16x-9)\\(5x^{3} (6x-9)^5)'=\underline{1215x^{2} (2x-3)^4(16x-9)}[/tex]
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Odpowiedź:
[tex]5x^{3} (6x-9)^5=5x^{3} [3(2x-3)]^5=5\cdot3^5x^3(2x-3)^5=1215x^3(2x-3)^5\\(x^{3} (2x-3)^5)'=(x^{3} )'(2x-3)^5+[(2x-3)^5]'\cdot x^{3} =\\3x^{2} (2x-3)^5+5\cdot2(2x-3)^4x^3=x^2(2x-3)^4[3(2x-3)+10x]=\\x^2(2x-3)^4(6x-9+10x)=x^2(2x-3)^4(16x-9)\\(5x^{3} (6x-9)^5)'=\underline{1215x^{2} (2x-3)^4(16x-9)}[/tex]