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

Problem

d()/d(x)*(4*ex−x2)

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*ex−x2)=(d(4)*ex)/d(x)−d(x2)/d(x)

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

(d(4)*ex)/d(x)=4d(ex)/d(x)

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

4d(ex)/d(x)=4*ex

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

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

5. Combine the results to find the final derivative.

4*ex−2*x

Final Answer

d()/d(x)*(4*ex−x2)=4*ex−2*x

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