Find the Derivative - d/dx square root of x^2+y^2

Problem

d(√(,x2+y2))/d(x)

Solution

1. Identify the function as a composition of an outer square root function and an inner polynomial function, requiring the use of the Chain Rule.

2. Apply the Power Rule to the outer function, treating the square root as an exponent of 1/2

3. Differentiate the inner function with respect to x treating y as a constant since the derivative is taken with respect to x

4. Multiply the derivative of the outer function by the derivative of the inner function.

d(√(,x2+y2))/d(x)=1/2*(x2+y2)(−1/2)⋅d(x2+y2)/d(x)

5. Compute the derivative of the inner part, where d(x2)/d(x)=2*x and d(y2)/d(x)=0

d(√(,x2+y2))/d(x)=1/(2√(,x2+y2))⋅2*x

6. Simplify the expression by canceling the factor of 2

d(√(,x2+y2))/d(x)=x/√(,x2+y2)

Final Answer

d(√(,x2+y2))/d(x)=x/√(,x2+y2)

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