Question

Y=log8(7x+2) найти производную функцию.больше обьяснений

Answer 1

y=log8(7x+2)
y' = 1/((7x+2)*ln(8))*(7x+2)' = 7/(ln(8) * (7x+2))

Answer 2

Это производная сложной функции, поэтому:
Y`=(log8(7x+2))` *(7x+2)`= 1/((7x+2)*ln8) *7= 7/((7x+2)*ln8)

Answer 3

Finding the Derivative of Y=log8(7x+2)

To find the derivative of the function Y=log8(7x+2), we can use the chain rule of differentiation. The chain rule states that if we have a composite function, such as f(g(x)), then the derivative is f'(g(x)) * g'(x), where f'(x) is the derivative of the outer function and g'(x) is the derivative of the inner function.

The derivative of Y=log8(7x+2) can be found as follows:

1. Let u = 7x+2 2. Then Y = log8(u)

Now, we can find the derivative of Y with respect to x using the chain rule:

Step 1: Find the derivative of Y with respect to u: - Y' = 1/(u * ln(8))

Step 2: Find the derivative of u with respect to x: - u' = 7

Step 3: Apply the chain rule: - Y' = Y' * u' - Y' = (1/(u * ln(8))) * 7 - Y' = 7/(u * ln(8))

Therefore, the derivative of Y=log8(7x+2) with respect to x is 7/(7x+2 * ln(8)).

This is the final result for the derivative of the given function.