Question

Найти производную функции: 7Inx-e^x/11

Answer 1

F(x)=7lnx-e^x/11
f′(x)=7/x-e^x/11=(77-e^x*x)/11x

Answer 2

To find the derivative of the given function, we'll use the rules of differentiation. Let's break down the function step by step and then apply the rules:

Given function: f(x) = 7ln(x) - e^x / 11

To find the derivative of this function, we'll differentiate each term separately. The rules we'll use are:

1. d/dx [ln(u)] = (1/u) * du/dx (where u is a function of x)
2. d/dx [e^u] = e^u * du/dx (where u is a function of x)
3. d/dx [c * u(x)] = c * du/dx (where c is a constant)

Now, let's proceed with differentiating the function:

Step 1: Differentiate 7ln(x) d/dx [7ln(x)] = 7 * (1/x) = 7/x

Step 2: Differentiate -e^x / 11 d/dx [-e^x / 11] = -(1/11) * d/dx [e^x] = -(1/11) * e^x

Now, combining both results, we get the derivative of the function:

f'(x) = 7/x - (1/11) * e^x

So, the derivative of the given function is 7/x - (1/11) * e^x.