Find the Derivative - d/dx 4x^(-3/8)

Problem

d()/d(x)*4*x(−3/8)

Solution

1. Identify the constant and the power of x in the expression 4*x(−3/8)

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

3. Multiply the constant 4 by the exponent −3/8

4⋅−3/8=−12/8

4. Simplify the resulting coefficient by dividing the numerator and denominator by their greatest common divisor, 4

−12/8=−3/2

5. Subtract 1 from the original exponent to find the new exponent.

−3/8−1=−3/8−8/8

−3/8−8/8=−11/8

6. Combine the new coefficient and the new exponent to write the final derivative.

Final Answer

(d(4)*x(−3/8))/d(x)=−3/2*x(−11/8)

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