Question

у=(8х-15)^5 найти производную функцию

Answer 1

y=(8х-15)^5

y'=5(8x-15)^4 * (8x-15)'=40(8x-15)^4

 

Answer 2

y=(8х-15)^5

y'=5(8x-15)^4 * (8x-15)'=40(8x-15)^4

Answer 3

Finding the Derivative of the Function

To find the derivative of the function \( u = (8x - 15)^5 \), we can use the chain rule of differentiation, which states that if \( u = f(g(x)) \), then \( \frac{du}{dx} = f'(g(x)) \cdot g'(x) \).

The derivative of the function \( u = (8x - 15)^5 \) can be found using the chain rule as follows:

1. Let \( f(x) = x^5 \) and \( g(x) = 8x - 15 \). 2. Find \( f'(x) \) and \( g'(x) \). 3. Apply the chain rule to find \( \frac{du}{dx} \).

Applying the Chain Rule

1. Find \( f'(x) \): - \( f'(x) = 5x^4 \). 2. Find \( g'(x) \): - \( g'(x) = 8 \). 3. Apply the chain rule: - \( \frac{du}{dx} = f'(g(x)) \cdot g'(x) \) - \( \frac{du}{dx} = 5(8x - 15)^4 \cdot 8 \) - \( \frac{du}{dx} = 40(8x - 15)^4 \)

Conclusion

The derivative of the function \( u = (8x - 15)^5 \) with respect to \( x \) is \( \frac{du}{dx} = 40(8x - 15)^4 \).