  We obtain a slowly rotating black hole solution in the scalar-tensor theory
of gravity with nonminimal derivative coupling to the Einstein tensor.
Properties of the obtained solution have been examined carefully. We also
investigate the thermodynamics of the given black hole. To obtain thermodynamic
functions, namely its entropy we use the Wald procedure which is suitable for
quite general diffeomorphism-invariant theories. The applied approach allowed
us to obtain the expression for entropy and the first law of black hole
thermodynamics. Having introduced thermodynamic pressure which is related to
the cosmological constant we have examined thermodynamics of the black hole in
the so called extended phase space. The extended phase space and specifically
chosen scalar `charge' allowed us not only to obtain the generalized first law
but also derive the Smarr relation. The behaviour of black hole's temperature,
heat capacity and Gibbs free energy shows a lot of similarities with the
behaviour of the corresponding values for Schwarzschild-AdS black hole in
standard General Relativity.
