Find the Derivative - d/dx y=x-x^7

Problem

d()/d(x)*(x−x7)

Solution

1. Identify the expression to be differentiated, which is a polynomial consisting of two terms: x and −x7

2. Apply the sum rule for derivatives, which states that the derivative of a sum or difference is the sum or difference of the derivatives.

3. Apply the power rule to the first term, x1 The derivative is 1⋅x(1−1) which simplifies to 1

4. Apply the power rule to the second term, −x7 The derivative is −7⋅x(7−1) which simplifies to −7*x6

5. Combine the results to find the final derivative.

Final Answer

d()/d(x)*(x−x7)=1−7*x6

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