Find the Derivative - d/dx y=20 square root of x

Problem

d()/d(x)*20√(,x)

Solution

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

y=20*x(1/2)

2. Apply the constant multiple rule, which states that the derivative of a constant times a function is the constant times the derivative of the function.

d(y)/d(x)=20⋅d(x(1/2))/d(x)

3. Apply the power rule, d(xn)/d(x)=n*x(n−1) where n=1/2

d(y)/d(x)=20⋅1/2*x(1/2−1)

4. Simplify the expression by multiplying the constants and calculating the new exponent.

d(y)/d(x)=10*x(−1/2)

5. Rewrite the expression using positive exponents and radical notation.

d(y)/d(x)=10/√(,x)

Final Answer

d()/d(x)*20√(,x)=10/√(,x)

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