Find the Derivative - d/dx y = square root of 7+9x

Problem

d()/d(x)√(,7+9*x)

Solution

1. Identify the function as a composition of functions, where the outer function is the square root u(1/2) and the inner function is u=7+9*x

2. Apply the power rule and the chain rule, which states that d()/d(x)*ƒ*(g(x))=ƒ′*(g(x))⋅g(x)′

3. Differentiate the outer function with respect to the inner function.

d()/d(x)*(7+9*x)(1/2)=1/2*(7+9*x)(−1/2)⋅d()/d(x)*(7+9*x)

4. Differentiate the inner function 7+9*x with respect to x

d(7+9*x)/d(x)=9

5. Multiply the results together to find the derivative.

d(y)/d(x)=1/2*(7+9*x)(−1/2)⋅9

6. Simplify the expression by moving the negative exponent to the denominator and combining constants.

d(y)/d(x)=9/(2√(,7+9*x))

Final Answer

d(√(,7+9*x))/d(x)=9/(2√(,7+9*x))

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