Question

F'x=(√2x+5)'

Answer 1

(√2x+5)'= (2x+5)'/2 (√2x+5)=2/2 (√2x+5)=1/(√2x+5)

Answer 2

To find the derivative of the function f(x) = √(2x + 5), we can use the chain rule. The chain rule states that if we have a composite function f(g(x)), the derivative is given by the product of the derivative of the outer function evaluated at the inner function and the derivative of the inner function.

Let's start by identifying the inner function and the outer function in this case: Inner function: g(x) = 2x + 5 Outer function: f(u) = √u, where u = 2x + 5

Now, we can find the derivatives of the inner and outer functions separately and apply the chain rule.

Derivative of the inner function: g'(x) = d/dx(2x + 5) = 2

Derivative of the outer function: f'(u) = d/du(√u) = (1/2)u^(-1/2) = (1/2)√(1/u) = (1/2)√(1/(2x + 5))

Applying the chain rule: f'(x) = f'(u) * g'(x) = (1/2)√(1/(2x + 5)) * 2 = √(1/(2x + 5))

Therefore, the derivative of the function f(x) = √(2x + 5) is f'(x) = √(1/(2x + 5)).