How to differentiate y=(x^2+4x)^5

To differentiate y=(x²+4x)⁵ you need to use the chain rule. The chain rule uses the fact that dy/dx = dy/dt * dt/dx. 

Here we create a new variable t, where t = x²+4x. Substituting this in the original equation gives y=t⁵. 

Differentiating t=x²+4x with respect to x; dt/dx = 2x+4

Differentiating y=t⁵ with respect to t; dy/dt = 5t⁴

We can combine these two equations to find dy/dx, as the chain rule states dy/dx = dy/dt * dt/dx.

This gives dy/dx = 5t⁴*(2x+4)

Substituting in our value of t, gives the final answer dy/dx = 5(x²+4x)⁴(2x+4)