Question

Write the function in the form y=f(u) and u=g(x). Then find d y/d x as a function of x.

y= ⁴ x
u=__

Answer 1

The function is y=4x and the variable u is equal to u=⁴√x. To find dy/dx, we express y as a function of u and u as a function of x. The derivative dy/dx is equal to (⁴√x)^(-3/4) * d⁴√x/dx.

Step-by-step explanation:

The given function is y = 4x and the variable u is equal to u = ⁴√x. To find dy/dx, we need to express y as a function of u and u as a function of x. In this case, we have:

y = 4(⁴√x)

Now, let's differentiate the equation with respect to x to find dy/dx:

dy/dx = d(4(⁴√x))/dx

= 4 * d(⁴√x)/dx

= 4 * (1/4)(⁴√x)^(-3/4) * d⁴√x/dx

= (⁴√x)^(-3/4) * d⁴√x/dx

Therefore, dy/dx = (⁴√x)^(-3/4) * d⁴√x/dx.