Evaluate the Derivative at x=0 y = square root of 5+9x , x=0

Problem

d(√(,5+9*x))/d(x)* at *x=0

Solution

1. Rewrite the function using a fractional exponent to make it easier to differentiate.

y=(5+9*x)^(1/2)

2. Apply the chain rule by taking the derivative of the outer function and multiplying it by the derivative of the inner function.

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

3. Differentiate the inner expression 5+9*x with respect to x

d(y)/d(x)=1/2*(5+9*x)^(−1/2)⋅9

4. Simplify the derivative expression into a single fraction.

d(y)/d(x)=9/(2√(,5+9*x))

5. Substitute x=0 into the derivative to find the specific value.

d(y)/d(x)=9/(2√(,5+9*(0)))

6. Calculate the final numerical value.

d(y)/d(x)=9/(2√(,5))

Final Answer

d(√(,5+9*x))/d(x)|=9/(2√(,5))

Want more problems? Check here!