Question

Differentiate:

Answer 1

\[\LARGE y= (3x+1)^2\]

Answer 2

2(3x+1)X3
=18x+6

Answer 3

(dy/dx)=18x+6

Answer 4

Simplified, yes. Thank you :)

Answer 5

Remember the derivative of a composite function:
if we have a function the derivative is :
\[y=g(x)^{m}\]
\[y'=m.g(x)^{m-1}g'(x)\]

So looking at the problem, it has pretty much the same structure:
\[y=(3x+1)^{2}\]
So following the derivative of a composite function (wich I didin't prove, just stated), the derivative should be, first derivating the function as if it was a single variable, and then multiplying by the derivative of the enclosed function:
\[y'=2(3x+1)(3)\]
applying distributive and multiplying we get:
\[y'=(6x+2)(3)\]
\[y'=18x+6\]

Answer 6

@harpreetsk Please never use "X" to indicate multiplication. VERY confusing. Usually "*" is clear enough. Oftentimes, simple juxtaposition is sufficient.

Glad you're here on the job.

Answer 7

thank for suggestion i will keep it in mind :)