Find the Derivative - d/dx y = natural log of square root of x+7

Problem

d()/d(x)*ln(√(,x+7))

Solution

1. Rewrite the expression using the properties of logarithms and exponents to simplify the differentiation process.

√(,x+7)=(x+7)(1/2)

2. Apply the power rule for logarithms, ln(ab)=b*ln(a) to move the exponent in front of the natural log.

ln((x+7)(1/2))=1/2*ln(x+7)

3. Differentiate the simplified expression using the constant multiple rule and the rule for the derivative of a natural logarithm, d(ln(u))/d(x)=1/ud(u)/d(x)

d()/d(x)1/2*ln(x+7)=1/2⋅1/(x+7)⋅d(x+7)/d(x)

4. Evaluate the derivative of the inner function x+7 which is 1

d(x+7)/d(x)=1

5. Multiply the remaining factors to find the final derivative.

1/2⋅1/(x+7)⋅1=1/(2*(x+7))

Final Answer

d()/d(x)*ln(√(,x+7))=1/(2*x+14)

Want more problems? Check here!