Differentiate y=(3x+1)^(2).

Question

Differentiate  y=(3x+1)^(2).

Bytelearn · Accepted Answer

Identify Functions: We are given the function y = (3x + 1)^2 and we need to find its derivative with respect to x. We will use the chain rule, which states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function times the derivative of the inner function.Derivative of Outer Function: Let's identify the outer function and the inner function. The outer function is u^2 and the inner function is u = 3x + 1. We will first take the derivative of the outer function with respect to u, which is 2u.Derivative of Inner Function: Now we will take the derivative of the inner function with respect to x, which is the derivative of 3x + 1. The derivative of 3x is 3, and the derivative of a constant (1) is 0. So, the derivative of the inner function is 3.Apply Chain Rule: Applying the chain rule, we multiply the derivative of the outer function by the derivative of the inner function. This gives us 2u * 3, where u is the inner function (3x + 1).Substitute back into Equation: Substitute u back into the equation to get the derivative in terms of x. This gives us 2(3x + 1) * 3.Simplify Expression: Now we simplify the expression. Multiply 2 by 3 to get 6, and then distribute it to the terms inside the parentheses: 6 * (3x + 1) = 6 * 3x + 6 * 1.Final Derivative: Simplify the expression further to get the final derivative: 18x + 6.

Differentiate $y=(3x+1)^{2}$ .

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Differentiate $y=(3x+1)^{2}$ .