Find the Derivative - d/dx 3x+7

Problem

d()/d(x)*(3*x+7)

Solution

1. Apply the sum rule for derivatives, which states that the derivative of a sum is the sum of the derivatives.

d()/d(x)*(3*x+7)=(d(3)*x)/d(x)+d(7)/d(x)

2. Apply the constant multiple rule to the first term by pulling the constant 3 out of the derivative.

(d(3)*x)/d(x)=3d(x)/d(x)

3. Differentiate the power function x using the power rule, where the derivative of x is 1

3d(x)/d(x)=3*(1)=3

4. Differentiate the constant 7 The derivative of any constant value is 0

d(7)/d(x)=0

5. Combine the results to find the final derivative.

3+0=3

Final Answer

d()/d(x)*(3*x+7)=3

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