Question

Find dy/dx if y=3x(x-2)

Answer 1

Answer:

solution dy/dx = 3x^2 - 6x

then y = 6x - 6 dy/dx

Step-by-step explanation:

hope answer the question .

Answer 2

Given: y=3x(x-2)

To find The value of dy/dx

Solution: In maths, there is a branch to study and that is calculus. The differentiation is one such part of the calculus that can be defined as the technique of locating the derivatives of a particular function. It is denoted by dy/dx, the rate of change of variable x with respect to variable y is designated as dy/dx. Differentiation follows a certain list of formulas for its execution.

∴y=3x(x-2)  [given above]

⇒y=3x²-6x

Now, differentiating both sides, we have

dy/dx={(3×2)x^(2-1) -(6×1)x^(1-1)} [∵ for y, differentiation of the rate of  

                                    change of variable x with respect to y]

               [formula used in right-hand side is d/dx=nx^(n-1), n is an integer]

⇒dy/dx=6x^1-6x^0

⇒dy/dx=6x-(6×1)   [∵x^0=1(law of indices)]

⇒dy/dx=6(x-1)    [taking 6 as common from 6x-6]

Thus, the value of dy/dx is 6(x-1).