Find the Derivative - d/dx 10x^5-8x+6e^x-10

Problem

d()/d(x)*(10*x5−8*x+6*ex−10)

Solution

1. Apply the sum and difference rule for derivatives, which allows for the differentiation of each term individually.

d()/d(x)*(10*x5)−d()/d(x)*(8*x)+d()/d(x)*(6*ex)−d()/d(x)*(10)

2. Apply the power rule to the first two terms, where d(xn)/d(x)=n*x(n−1)

(d(10)*x5)/d(x)=50*x4

(d(8)*x)/d(x)=8

3. Apply the exponential rule to the third term, noting that the derivative of ex is ex

(d(6)*ex)/d(x)=6*ex

4. Apply the constant rule to the final term, as the derivative of any constant is zero.

d(10)/d(x)=0

5. Combine the results to find the final derivative expression.

50*x4−8+6*ex

Final Answer

d()/d(x)*(10*x5−8*x+6*ex−10)=50*x4−8+6*ex

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