<p>We investigate the cosmic inflation within a class of the scalar-tensor model with the scalar-dependent non-minimal kinetic couplings. The inflationary dynamical potential will be applied. Using the slow-roll approximation, we compute theoretical predictions for the key observables, like the spectral indexes <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(n_s\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>n</mi> <mi>s</mi> </msub> </math></EquationSource> </InlineEquation>, scalar-to-tensor ratio <i>r</i> and the running of the scalar spectral index <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\alpha _s\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>α</mi> <mi>s</mi> </msub> </math></EquationSource> </InlineEquation> in terms of the free parameters of the model. Besides, we find the limitations of these parameters. In addition, these quantities will be compared with the latest observational data from the Planck data. Furthermore, we analyze the sensitivity of <i>r</i>, <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(n_s\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>n</mi> <mi>s</mi> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\alpha _s\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>α</mi> <mi>s</mi> </msub> </math></EquationSource> </InlineEquation> in terms of the model’s free parameters.</p>