Find the Derivative - d/dx y=3x^2+4x

Problem

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

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

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

3. Apply the power rule d(xn)/d(x)=n*x(n−1) to each term.

3*(2*x(2−1))+4*(1*x(1−1))

4. Simplify the exponents and coefficients to find the final derivative.

6*x+4

Final Answer

d()/d(x)*(3*x2+4*x)=6*x+4

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