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diff --git a/src/main/java/org/apache/commons/math3/analysis/DifferentiableMultivariateFunction.java b/src/main/java/org/apache/commons/math3/analysis/DifferentiableMultivariateFunction.java
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+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.commons.math3.analysis;
+
+/**
+ * Extension of {@link MultivariateFunction} representing a differentiable multivariate real
+ * function.
+ *
+ * @since 2.0
+ * @deprecated as of 3.1 replaced by {@link
+ *     org.apache.commons.math3.analysis.differentiation.MultivariateDifferentiableFunction}
+ */
+@Deprecated
+public interface DifferentiableMultivariateFunction extends MultivariateFunction {
+
+    /**
+     * Returns the partial derivative of the function with respect to a point coordinate.
+     *
+     * <p>The partial derivative is defined with respect to point coordinate x<sub>k</sub>. If the
+     * partial derivatives with respect to all coordinates are needed, it may be more efficient to
+     * use the {@link #gradient()} method which will compute them all at once.
+     *
+     * @param k index of the coordinate with respect to which the partial derivative is computed
+     * @return the partial derivative function with respect to k<sup>th</sup> point coordinate
+     */
+    MultivariateFunction partialDerivative(int k);
+
+    /**
+     * Returns the gradient function.
+     *
+     * <p>If only one partial derivative with respect to a specific coordinate is needed, it may be
+     * more efficient to use the {@link #partialDerivative(int)} method which will compute only the
+     * specified component.
+     *
+     * @return the gradient function
+     */
+    MultivariateVectorFunction gradient();
+}