Find the Derivative - d/dx y=(8x^3)/3-7x

Problem

d()/d(x)*((8*x3)/3−7*x)

Solution

1. Identify the expression as a difference of two terms and apply the sum/difference rule for derivatives.

d()/d(x)*((8*x3)/3−7*x)=d()/d(x)(8*x3)/3−d()/d(x)*7*x

2. Apply the power rule d(xn)/d(x)=n*x(n−1) to the first term, treating the fraction 8/3 as a constant coefficient.

d()/d(x)(8*x3)/3=8/3⋅3*x2

3. Simplify the first term by canceling the common factor of 3

8/3⋅3*x2=8*x2

4. Apply the power rule to the second term, noting that the derivative of x is 1

(d(7)*x)/d(x)=7

5. Combine the results of the derivatives to find the final expression.

d(y)/d(x)=8*x2−7

Final Answer

d()/d(x)*((8*x3)/3−7*x)=8*x2−7

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