Find the Derivative - d/dx square root of x^7

Problem

d(√(,x7))/d(x)

Solution

1. Rewrite the radical expression using a fractional exponent. The square root of a power is equivalent to raising the base to the power divided by 2.

√(,x7)=x(7/2)

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

d(x(7/2))/d(x)=7/2*x(7/2−1)

3. Simplify the exponent by performing the subtraction.

7/2−1=7/2−2/2=5/2

4. Convert the expression back into radical form if desired.

7/2*x(5/2)=(7√(,x5))/2

Final Answer

d(√(,x7))/d(x)=7/2*x(5/2)

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