Question

If y=f(u)=7u+11 and u=g(x)=4/5x⁵, then by the chain rule, (dy)/(dx)

Answer 1

To find (dy)/(dx), we can use the Chain Rule. By differentiating u with respect to x and v with respect to u, we can multiply the two derivatives together to find (dy)/(dx). In this case, (dy)/(dx) = 28x^4.

Step-by-step explanation:

Let's start by finding (du)/(dx) and (dv)/(du).

Given that u = (4/5)x^5, we can differentiate u with respect to x to get:

(du)/(dx) = (4/5)(5x^4) = 4x^4

Next, we differentiate v = 7u + 11 with respect to u to get:

(dv)/(du) = 7

Now, we can apply the Chain Rule by multiplying (du)/(dx) and (dv)/(du) to get the derivative of y = f(u) = 7u + 11 with respect to x:

(dy)/(dx) = (dv)/(du) * (du)/(dx) = 7 * 4x^4 = 28x^4