Find the Derivative - d/dx (2x^2)/5

Problem

d()/d(x)(2*x2)/5

Solution

1. Identify the constant coefficient in the expression. The expression (2*x2)/5 can be rewritten as 2/5⋅x2

2. Apply the constant multiple rule, which states that d()/d(x)*[c⋅ƒ(x)]=c⋅d(ƒ(x))/d(x)

3. Apply the power rule to the term x2 The power rule states that d(xn)/d(x)=n*x(n−1)

4. Calculate the derivative of x2 which is 2*x

5. Multiply the constant coefficient by the result of the power rule.

2/5⋅2*x=(4*x)/5

Final Answer

d()/d(x)(2*x2)/5=(4*x)/5

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