The derivative of 𝑦 = √𝑥2+33𝑥 isA) 𝑑𝑦𝑑𝑥 = −𝑥2−93𝑥2(𝑥2+3)2 3⁄ B) 𝑑𝑦𝑑𝑥 = −3𝑥2(𝑥2+3)2 3⁄C) 𝑑𝑦𝑑𝑥 = 3𝑥2(𝑥2+3)2 3⁄ D) 𝑑𝑦𝑑𝑥 = 𝑥2+93𝑥2(𝑥2+3)2 3⁄E) None of the aboveDownloaded by Lindelwa Madi ([email protected])

To find the derivative of the function y = √(x² + 33x), we first need to rewrite the function in a form that is easier to differentiate. We can rewrite the square root as a power of 1/2, so the function becomes y = (x² + 33x)^(1/2).

Now we can use the chain rule to differentiate this function. The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function.

The outer function is u^(1/2) and its derivative is (1/2)u^(-1/2). The inner function is u = x² + 33x and its derivative is 2x + 33.

Applying the chain rule, we get:

dy/dx = (1/2)(x² + 33x)^(-1/2) * (2x + 33)

Simplifying this expression, we get:

dy/dx = (2x + 33) / (2√(x² + 33x))

This option is not listed in the given choices, so the correct answer is E) None of the above.