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In this article, we construct a <inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msup><mi>C</mi><mn>1</mn></msup></semantics></math></inline-formula> stable invariant manifold for the delay differential equation <inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>x</mi><mo>′</mo></msup><mo>=</mo><mi>A</mi><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>+</mo><mi>L</mi><msub><mi>x</mi><mi>t</mi></msub><mo>+</mo><mi>f</mi><mrow><mo>(</mo><mi>t</mi><mo>,</mo><msub><mi>x</mi><mi>t</mi></msub><mo>)</mo></mrow></mrow></semantics></math></inline-formula> assuming the <inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>ρ</mi></semantics></math></inline-formula>-nonuniform exponential dichotomy for the corresponding solution operator. We also assume that the <inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msup><mi>C</mi><mn>1</mn></msup></semantics></math></inline-formula> perturbation, <inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>f</mi><mo>(</mo><mi>t</mi><mo>,</mo><msub><mi>x</mi><mi>t</mi></msub><mo>)</mo></mrow></semantics></math></inline-formula>, and its derivative are sufficiently small and satisfy smoothness conditions. To obtain the invariant manifold, we follow the method developed by Lyapunov and Perron. We also show the dependence of invariant manifold on the perturbation <inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>f</mi><mo>(</mo><mi>t</mi><mo>,</mo><msub><mi>x</mi><mi>t</mi></msub><mo>)</mo></mrow></semantics></math></inline-formula>.