Find the Derivative - d/dx 2x^2+3x

Problem

d()/d(x)*(2*x2+3*x)

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)*(2*x2+3*x)=(d(2)*x2)/d(x)+(d(3)*x)/d(x)

2. Apply the constant multiple rule to move the coefficients outside of the derivatives.

2d(x2)/d(x)+3d(x)/d(x)

3. Apply the power rule, which states that d(xn)/d(x)=n*x(n−1)

2*(2*x(2−1))+3*(1*x(1−1))

4. Simplify the exponents and multiply the constants.

4*x1+3*x0

5. Finalize the expression by noting that x1=x and x0=1

4*x+3

Final Answer

d()/d(x)*(2*x2+3*x)=4*x+3

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