Question

How do you differentiate `y =cos(3x+7)` using the chain rule?

Answer 1

`-3sin(3x+7)`

Explanation:

The chain rule: `d/dx[f(g(x))] = f'(g(x)) * g'(x)`

Essentially, you take the derivative of whatever is on the outside like normal then multiply it by whats on the inside of the trig function.

The derivative of `cos(x)` is `-sin(x)`
so taking the derivative of the outside gives us: `-sin(3x + 7)`
then we take the derivative of the inside: `d/dx[3x+7] = 3`

The derivative of the inside is then multiplied by our first derivative:

`-sin(3x+7) * 3 = -3sin(3x+7)`