Find the Derivative - d/dx (5x+2)^2

Problem

d(5*x+2)/d(x)

Solution

1. Identify the rule needed to differentiate the expression. Since we have a function (5*x+2) raised to a power, we use the chain rule, which states d(un)/d(x)=n*u(n−1)d(u)/d(x)

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

d(5*x+2)/d(x)=2*(5*x+2)(2−1)⋅d(5*x+2)/d(x)

3. Differentiate the inner function 5*x+2 with respect to x

d(5*x+2)/d(x)=5

4. Multiply the results together to find the derivative.

2*(5*x+2)1⋅5

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

10*(5*x+2)

6. Distribute the 10 into the parentheses.

50*x+20

Final Answer

d(5*x+2)/d(x)=50*x+20

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