Find the Derivative - d/dx ( square root of 10)/(x^7)

Problem

d()/d(x)√(,10)/(x7)

Solution

1. Rewrite the expression using a negative exponent to prepare for the power rule.

√(,10)/(x7)=√(,10)*x(−7)

2. Identify the constant factor √(,10) and move it outside the derivative.

(d(√(,10))*x(−7))/d(x)=√(,10)d(x(−7))/d(x)

3. Apply the power rule, which states that d(xn)/d(x)=n*x(n−1) where n=−7

d(x(−7))/d(x)=−7*x(−7−1)

4. Simplify the exponent and multiply by the constant factor.

√(,10)*(−7*x(−8))=−7√(,10)*x(−8)

5. Convert the expression back into fraction form by moving the variable to the denominator.

−7√(,10)*x(−8)=−(7√(,10))/(x8)

Final Answer

d()/d(x)√(,10)/(x7)=−(7√(,10))/(x8)

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