Find the Derivative - d/dx 4/(7x^3)

Problem

d()/d(x)4/(7*x3)

Solution

1. Rewrite the expression using a negative exponent to make it easier to differentiate.

4/(7*x3)=4/7*x(−3)

2. Apply the constant multiple rule by moving the constant coefficient outside of the derivative.

d()/d(x)4/7*x(−3)=4/7d(x(−3))/d(x)

3. Apply the power rule, which states that d(xn)/d(x)=n*x(n−1)

4/7*(−3*x(−3−1))=4/7*(−3*x(−4))

4. Multiply the constants and simplify the expression.

4/7⋅−3=−12/7

5. Rewrite the expression with a positive exponent by moving the variable back to the denominator.

−12/7*x(−4)=−12/(7*x4)

Final Answer

d()/d(x)4/(7*x3)=−12/(7*x4)

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