Find the Derivative - d/dx (7 square root of x)/8

Problem

d()/d(x)(7√(,x))/8

Solution

1. Rewrite the expression by pulling out the constant coefficient and converting the radical to an exponential form.

(7√(,x))/8=7/8*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()/d(x)7/8*x(1/2)=7/8d(x(1/2))/d(x)

3. Use 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.

7/8⋅1/2*x(−1/2)=7/16*x(−1/2)

5. Convert the expression back into radical form by moving the negative exponent to the denominator.

7/(16*x(1/2))=7/(16√(,x))

Final Answer

d()/d(x)(7√(,x))/8=7/(16√(,x))

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