Find the Derivative - d/dx 2/( fourth root of x^3)

Problem

d()/d(x)2/√(4,x3)

Solution

1. Rewrite the radical expression using a rational exponent.

√(4,x3)=x(3/4)

2. Move the variable to the numerator by applying the rule for negative exponents.

2/(x(3/4))=2*x(−3/4)

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

(d(2)*x(−3/4))/d(x)=2⋅(−3/4)*x(−3/4−1)

4. Simplify the coefficient and the exponent.

2⋅(−3/4)=−3/2

−3/4−1=−7/4

5. Convert the expression back into radical form with a positive exponent.

−3/2*x(−7/4)=−3/(2*x(7/4))

−3/(2*x(7/4))=−3/(2√(4,x7))

Final Answer

d()/d(x)2/√(4,x3)=−3/(2*x(7/4))

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