*Last updated: 2023-03-16.*
# tf_quant_finance.math.value_and_gradient
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Computes `f(*xs)` and its gradients wrt to `*xs`.
```python
tf_quant_finance.math.value_and_gradient(
f, xs, output_gradients=None, use_gradient_tape=False,
unconnected_gradients=None, name=None
)
```
#### Args:
* `f`: Python `callable` to be differentiated. If `f` returns a scalar, this
scalar will be differentiated. If `f` returns a tensor or list of tensors,
by default a scalar will be computed by adding all their values to produce
a single scalar. If desired, the tensors can be elementwise multiplied by
the tensors passed as the `dy` keyword argument to the returned gradient
function.
* `xs`: Python list of parameters of `f` for which to differentiate. (Can also
be single `Tensor`.)
* `output_gradients`: A `Tensor` or list of `Tensor`s the same size as the
result `ys = f(*xs)` and holding the gradients computed for each `y` in
`ys`. This argument is forwarded to the underlying gradient implementation
(i.e., either the `grad_ys` argument of `tf.gradients` or the
`output_gradients` argument of `tf.GradientTape.gradient`).
* `use_gradient_tape`: Python `bool` indicating that `tf.GradientTape` should be
used regardless of `tf.executing_eagerly()` status.
Default value: `False`.
* `unconnected_gradients`: An enum `tf.UnconnectedGradients` which specifies the
gradient value returned when the given input tensors are unconnected.
Default value: `None`, which maps to `tf.UnconnectedGradients.NONE`.
* `name`: Python `str` name prefixed to ops created by this function.
Default value: `None` (i.e., `'value_and_gradient'`).
#### Returns:
A tuple of two elements. The first one is a `Tensor` representing the value
of the function at `xs` and the second one is either a `Tensor` or a list of
`Tensor`s representing the gradient of `f(*xs)` wrt `xs`.
* `y`: `y = f(*xs)`.
* `dydx`: Gradient of `y` wrt each of `xs`.