How do I differentiate: (3x + 7)^2?
We can see that (3x + 7)2 is a 'composite function'. We can rewrite this as g(f(x)), where f(x) = 3x + 7 and g(x) = x2. As you will have learnt, you will need to use the chain rule for this type of differentiation. The chain rule is as follows: d/dx(g(f(x))) = d/d(f(x))(g(f(x)) * d/dx(f(x)). This problem can be broken down into 2 calculations. Let's work out each term individually:d/d(f(x))(g(f(x)):d/dx(g(x)) is simply 2x (bring the power down, reduce the power by one). Therefore we can substitute f(x) in as x in this equation which gives us d/d(f(x))(g(f(x)) = 2f(x) = 2*(3x + 7).d/dx(f(x)): We can see that this is 3 (from 3x, the constant 7 term disappears). Putting this all together gives our answer of:d/dx(g(f(x))) = d/d(f(x))(g(f(x)) * d/dx(f(x)) = (2*(3x + 7)) * 3 = 6*(3x + 7) = 18x + 42.
