Find the Derivative - d/dx y=10 square root of x

Problem

d()/d(x)*10√(,x)

Solution

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

√(,x)=x(1/2)

2. Apply the constant multiple rule, which allows the constant 10 to be moved outside the derivative.

(d(10)*x(1/2))/d(x)=10⋅d(x(1/2))/d(x)

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

d(x(1/2))/d(x)=1/2*x(1/2−1)

4. Simplify the exponent and the coefficients.

1/2*x(−1/2)

10⋅1/2*x(−1/2)=5*x(−1/2)

5. Convert the negative fractional exponent back into radical form.

x(−1/2)=1/√(,x)

5⋅1/√(,x)=5/√(,x)

Final Answer

(d(10)√(,x))/d(x)=5/√(,x)

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