Question

G(x)=Lg(√x+10) g'(x)=?

Answer 1

Ответ:

Пошаговое объяснение:

(1/((√x+10) ln10)*1/2x^(-1/2)

Answer 2

To find the derivative of the function G(x) = lg(√x + 10), where lg represents the logarithm base 10, we need to use the chain rule of differentiation. The chain rule states that if we have a composite function of the form f(g(x)), then the derivative of f(g(x)) with respect to x is given by f'(g(x)) * g'(x).

Let's differentiate G(x) step-by-step:

Step 1: Identify the inner function and its derivative. Inner function: g(x) = √x + 10 Derivative of the inner function: g'(x) = d/dx (√x + 10) = (1/2√x)

Step 2: Identify the outer function and its derivative. Outer function: f(u) = lg(u) where u = √x + 10 Derivative of the outer function: f'(u) = d/du lg(u) = (1 / (u * ln(10)))

Step 3: Combine the derivatives using the chain rule. G'(x) = f'(g(x)) * g'(x) G'(x) = (1 / (u * ln(10))) * (1/2√x) G'(x) = (1 / (√x + 10) * ln(10)) * (1/2√x) G'(x) = (1 / (2 * √x * (√x + 10) * ln(10)))

So, the derivative of G(x) with respect to x, denoted as G'(x), is (1 / (2 * √x * (√x + 10) * ln(10))).