Find the Derivative - d/dx (6x+1)^2

Problem

d(6*x+1)/d(x)

Solution

1. Identify the rule needed to differentiate the expression, which is the chain rule for a function of the form un

2. Apply the power rule to the outer function by bringing the exponent 2 to the front and decreasing the power by 1

2*(6*x+1)(2−1)

3. Apply the chain rule by multiplying the result by the derivative of the inner function 6*x+1

2*(6*x+1)1⋅d(6*x+1)/d(x)

4. Differentiate the inner expression 6*x+1 which results in 6

2*(6*x+1)⋅6

5. Simplify the expression by multiplying the constants 2 and 6

12*(6*x+1)

6. Distribute the constant to reach the final expanded form.

72*x+12

Final Answer

d(6*x+1)/d(x)=72*x+12

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