Backpropagation through an activation function is a core step in training neural networks, where you compute how the loss changes with respect to the pre-activation values. In this problem you’ll implement the backward pass for a common activation so gradients can flow from later layers to earlier ones.

Requirements

Implement the function

Rules:

• Use the chain rule to compute ( dZ = dA \odot g'(Z) ), where (g) is the activation and (\odot) is elementwise multiply.
• If activation == "relu", use ( g'(z) = 1 ) when ( z > 0 ) else ( 0 ).
• If activation == "sigmoid", use ( \sigma(z) = \frac{1}{1 + e^{-z}} ) and ( \sigma'(z) = \sigma(z)\bigl(1-\sigma(z)\bigr) ).
• Return the result as a NumPy array.
• Don’t call any deep learning frameworks (no PyTorch/TensorFlow); just NumPy + built-ins.

Example

Output: