Question

Differentiate y = 3x(5x² - x)²

Answer 1

Given:

`y=3x(5x^2-x)^2`

Required:

To differentiate the given equation.

Step-by-step explanation:

Consider

`\begin{gathered} y=3x(5x^2-x)^2 \\ \\ (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}`

Final Answer:

`(dy)/(dx)=165x^4-120x^3+9x^2`