Find the Derivative - d/dx (3x^2)/7

Problem

d()/d(x)(3*x^2)/7

Solution

1. Identify the constant coefficient in the expression. The term (3*x^2)/7 can be rewritten as 3/7⋅x^2

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

3. Differentiate the power function x^2 using the power rule, d(x^n)/d(x)=n*x^(n−1)

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

4. Multiply the constant coefficient by the derivative of the power function.

3/7⋅2*x=(6*x)/7

Final Answer

d()/d(x)(3*x^2)/7=(6*x)/7

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