Find the Derivative - d/dx 9/(8 fourth root of x^3)

Problem

d()/d(x)9/(8√(4,x3))

Solution

1. Rewrite the radical expression using a fractional exponent.

√(4,x3)=x(3/4)

2. Move the variable to the numerator by changing the sign of the exponent.

9/(8*x(3/4))=9/8*x(−3/4)

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

d()/d(x)9/8*x(−3/4)=9/8⋅(−3/4)*x(−3/4−1)

4. Simplify the coefficient and the exponent.

9/8⋅(−3/4)=−27/32

−3/4−1=−7/4

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

−27/32*x(−7/4)=−27/(32*x(7/4))

−27/(32*x(7/4))=−27/(32√(4,x7))

Final Answer

d()/d(x)9/(8√(4,x3))=−27/(32√(4,x7))

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