Find the Derivative - d/dx y = square root of x+4

Problem

d()/d(x)√(,x+4)

Solution

1. Rewrite the square root expression using a fractional exponent to make it easier to apply power rules.

√(,x+4)=(x+4)(1/2)

2. Apply the power rule and the chain rule, where the derivative of un is n*u(n−1)⋅d(u)/d(x)

d(x+4)/d(x)=1/2*(x+4)(−1/2)⋅d(x+4)/d(x)

3. Differentiate the inner function x+4 with respect to x

d(x+4)/d(x)=1

4. Simplify the expression by multiplying the terms and moving the negative exponent to the denominator.

1/2*(x+4)(−1/2)⋅1=1/(2√(,x+4))

Final Answer

d(√(,x+4))/d(x)=1/(2√(,x+4))

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