Question

If f(x) and g(x) are differentiable functions such that f(1)=10, f '(1)=11, f '(15)=12, g(1)=15, g '(1)=14, g '(2)=15, g '(5) = 16, find d/dx f(g(x)) | x=1.

Answer 1

To find d/dx f(g(x)) | x=1, you need to apply the chain rule. The result is 154.

Step-by-step explanation:

To find d/dx f(g(x)) | x=1, we need to apply the chain rule. The chain rule states that if we have a composition of functions, the derivative of the composition is the product of the derivatives of the individual functions.

1. First, we differentiate the outer function f(g(x)) with respect to g(x), which gives us f'(g(x)).
2. Then, we differentiate the inner function g(x) with respect to x, which gives us g'(x).
3. Finally, we substitute x=1 into both derivatives and multiply them together to get the final result, f'(g(x)) * g'(x).

In this case, we have f'(1) * g'(1) which is 11 * 14 = 154.