
Evaluating the Jvp for  yields the result:

We can execute the same expression in PyTorch and calculate the gradient of the input:

>>> import torch
>>> x = torch.tensor([0.5, 0.75], requires_grad=True)
>>> y = torch.log(x[0] * x[1]) * torch.sin(x[1])
>>> y.backward(1.0)
>>> x.grad
  tensor([1.3633,
          0.1912])