Ralf,
I like this problem. I'm going to do one like it for you, but with three parts.
Find the derivative of the function
1 . y = 3  5x^{4}
2 . y = 3  (5x)^{4}
3 . y = (3  5x )^{4}
 This is an application of the first properties of differentiation. the derivative of a constant is zero, the derivative of x^{r} is rx^{r1} and if k is a constant and f(x) is a differentiable function then the derivative of k f(x) is k f '(x). Thus the derivative of y = 3  5x^{4} is dy/dx = 5 (4x^{3}) = 20 x^{3}.
 For the second problem you need the properties I stated before plus the chain rule. One special case of the chain rule is that if f(x) is a differentiable function and k is a constant then the derivative of (f(x))^{k} is k (f(x))^{k1} f '(x). Hence the derivative of y = 3  (5x)^{4} is dy/dx = 4 (5x)^{3} × 5 = 20 (5x)^{3}.
 This is an application of the chain rule again. Since the derivative of 3  5x is 5 the derivative of y = (3  5x )^{4} is dy/dx = 4(3  5x)^{3} × (5) = 20 (3  5x)^{3}
I hope this helps,
Harley
