Question

Write the function below in the form y = f(u) and u = g(x), then find dy/ dx as a function of x.

y = (7x + 15)⁵
Write y = (7x + 15)⁵ in the form y = f(u) and u = g(x).

Answer 1

To write the function y = (7x + 15)⁵ in the form y = f(u) and u = g(x), we can let u = 7x + 15. This means that y = u⁵. Using the chain rule, the derivative dy/dx is found to be 5(7x + 15)⁴ * 7.

Step-by-step explanation:

To write the function y = (7x + 15)⁵ in the form y = f(u) and u = g(x), we can let u = 7x + 15. This means that y = u⁵.

Next, we need to find dy/dx as a function of x. We can use the chain rule to differentiate y = u⁵ with respect to x. The chain rule states that dy/dx = dy/du * du/dx. Evaluating the derivatives, we get dy/dx = 5u⁴ * 7. Substituting u = 7x + 15 back in, we have dy/dx = 5(7x + 15)⁴ * 7.