Given:
[tex]y=3x(5x^2-x)^2[/tex]Required:
To differentiate the given equation.
Explanation:
Consider
[tex]\begin{gathered} y=3x(5x^2-x)^2 \\ \\ \frac{dy}{dx}=3x(2)(5x^2-x)(10x-1)+(5x^2-x)^23 \\ \\ =6x(15x^3-5x^2-10x^2+x)+3(25x^4+x^2-10x^3) \\ \\ =90x^4-90x^3+6x^2+75x^4+3x^2-30x^3 \\ \\ =165x^4-120x^3+9x^2 \end{gathered}[/tex]Final Answer:
[tex]\frac{dy}{dx}=165x^4-120x^3+9x^2[/tex]