Find the Derivative - d/dx 4e^x-x^2

Problem

d()/d(x)*(4*e^x−x^2)

Solution

1. Apply the sum/difference rule of differentiation, which allows for the derivative of each term to be taken separately.

d()/d(x)*(4*e^x−x^2)=(d(4)*e^x)/d(x)−d(x^2)/d(x)

2. Apply the constant multiple rule to the first term, moving the constant 4 outside of the derivative.

(d(4)*e^x)/d(x)=4d(e^x)/d(x)

3. Differentiate the exponential function using the rule d(e^x)/d(x)=e^x

4d(e^x)/d(x)=4*e^x

4. Apply the power rule to the second term, d(x^n)/d(x)=n*x^(n−1) where n=2

d(x^2)/d(x)=2*x

5. Combine the results to find the final derivative.

4*e^x−2*x

Final Answer

d()/d(x)*(4*e^x−x^2)=4*e^x−2*x

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