Find the Derivative - d/dx (8x+1)^2

Problem

d()/d(x)*(8*x+1)2

Solution

1. Identify the rule needed to differentiate the expression, which is the Power Rule combined with the Chain Rule for a function of the form un

2. Apply the Power Rule by bringing the exponent 2 to the front and decreasing the power by 1

d(8*x+1)/d(x)=2*(8*x+1)(2−1)⋅d(8*x+1)/d(x)

3. Differentiate the inner function 8*x+1 with respect to x

d(8*x+1)/d(x)=8

4. Substitute the derivative of the inner function back into the expression.

2*(8*x+1)1⋅8

5. Simplify the expression by multiplying the constants 2 and 8

16*(8*x+1)

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

128*x+16

Final Answer

d(8*x+1)/d(x)=128*x+16

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