Find dy/dx y = square root of 5-9x

Problem

d()/d(x)√(,5−9*x)

Solution

1. Identify the function as a composition of functions where y=√(,u) and u=5−9*x

2. Rewrite the square root as a power to prepare for differentiation using the power rule.

y=(5−9*x)(1/2)

3. Apply the chain rule, which states that d(y)/d(x)=d(y)/d(u)⋅d(u)/d(x)

d(y)/d(x)=1/2*(5−9*x)(−1/2)⋅d(5−9*x)/d(x)

4. Differentiate the inner function 5 - 9xw*i*t*h*r*e*s(p)*e*c*t*t*o$.

d(5−9*x)/d(x)=−9

5. Substitute the derivative of the inner function back into the expression.

d(y)/d(x)=1/2*(5−9*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√(,5−9*x))

Final Answer

d(y)/d(x)=−9/(2√(,5−9*x))

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