Find the Derivative - d/d@VAR f(x)=1/( square root of x^17)

Problem

d()/d(x)1/√(,x17)

Solution

1. Rewrite the expression using rational exponents. The square root of a power is equivalent to that power raised to the 1/2 so √(,x17)=x17/2

2. Apply the rule for negative exponents to move the term to the numerator, which gives x(−17/2)

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

4. Substitute n=−17/2 into the power rule formula.

5. Subtract 1 from the exponent: −17/2−1=−17/2−2/2=−19/2

6. Simplify the final expression by moving the negative exponent back to the denominator.

Final Answer

d()/d(x)1/√(,x17)=−17/(2*x19/2)

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