Have any drugs been shown to increase the neuroplasticity of adult brains? I read recently in the book "meet your happy chemicals" that the hormones of puberty are neurochemicals that cause your neurons to connect and myelinate more easily.

If this is true have any studies been done to see if injecting those same hormones into the body of an adult enables a similar rate of accelerated learning?
I read recently in the book &quot;meet your happy chemicals&quot; that the hormones of puberty are neurochemicals that cause your neurons to connect and myelinate more easily.

I will presume that you're referring to brain-derived neurotrophic factor (BDNF) which is involved in neurogenesis and neuroplasticity.

If this is true have any studies been done to see if injecting those same hormones into the body of an adult enables a similar rate of accelerated learning?

You may want to look into Cerebrolysin which is an injectable preparation of fractionate porcine brain. Essentially they take pig brains, spin them in a centrifuge and extract the heavy fraction that contains the neuropepties, including BDNF.
Enclosed is some of the research. There is evidence that Cerebrolysin facilitates neurogenesis and neuroplasticity, but to my knowledge, does not promote learning or cognitive performance in healthy individuals.
Properties of Cerebrolysin
Here's a brief summary Cerebrolysin's effects on the brain:

Cerebrolysin (Cbl) is the only drug available for clinical use containing active fragments of important neurotrophic factors. The active fragments are small neuropeptides which cross the blood-brain barrier (BBB) and mimic the action of endogenous neurotrophic factors such as BDNF, GDNF, CNTF and NGF and others. The neurotrophic action of the Cbl helps in the survival of neurons and prevents the cell death. In addition, several reports suggest that Cbl induces neuroprotection when there is a damage of the brain and also induce neurogenesis. These two actions (neuroprotection and neurogenesis) maintain... In addition, recent reports suggest that Cbl increases synaptic communication by increasing dendritic arborization as well as the number of dendritic spines in cortical regions such as PFC and hippocampus.

Flores, G., &amp; Atzori, M. (2014). The potential of cerebrolysin in the treatment of schizophrenia. Pharmacology &amp; Pharmacy, 5, 691–704. https://doi.org/10.4236/pp.2014.57079
Pharmacotherapy in Alzheimer's disease
Here's one on Alzheimer's disease:

Cerebrolysin is a neuropeptide preparation mimicking the action of
endogenous neurotrophic factors. Positive effects of Cerebrolysin on
β-amyloid- and tau-related pathologies, neuroinflammation,
neurotrophic factors, oxidative stress, excitotoxicity,
neurotransmission, brain metabolism, neuroplasticity, neuronal
apoptosis and degeneration, neurogenesis and cognition were
demonstrated in experimental conditions... The clinical efficacy of Cerebrolysin in Alzheimer's disease
was evaluated in several randomized, double-blind, clinical trials,
showing consistent benefits on global clinical function and cognition,
improvements in behavior at high doses, and minor effects on daily
living activities in patients with mild to moderate Alzheimer's
disease, as well as in subgroups of moderate to moderately severe
patients.

Alvarez, X. A., &amp; Fuentes, P. (2011). Cerebrolysin in Alzheimer’s disease. Drugs of Today, 47, 487. https://doi.org/10.1358/dot.2011.47.7.1656496
The main problem with all the studies with Cerebrolysin or other candidate drugs is that even though the study findings may be statistically significant the effect sizes are nothing to write home about. Though granted, to some, even incremental benefit is better than no benefit at all.
Recovery from stroke
This one demonstrates efficacy in recovery of motor control following stroke:

Cerebrolysin is a neuropeptide preparation with neuroprotective and neurorestorative effects. Combining Cerebrolysin
treatment with a standardized rehabilitation program may have a
potential synergistic effect in the subacute stage of stroke. This
study aims to evaluate whether Cerebrolysin provides additional motor
recovery on top of rehabilitation therapy in the subacute stroke
patients with moderate to severe motor impairment...
In the stroke patients with severe motor
impairment, the Cerebrolysin group exhibited significantly more
improvement in motor function compared with the placebo group. Effects of Cerebrolysin were demonstrated as restricted
increments of corticospinal diffusivity and as recovery of the
sensorimotor connectivity... The combination of standard rehabilitation therapy with Cerebrolysin treatment in the subacute stroke has shown additional benefit on motor recovery and plastic changes of the corticospinal
tract in patients with severe motor impairment.

Chang, W. H., Park, C., Kim, D. Y., Shin, Y.-I., Ko, M.-H., Lee, A., … Kim, Y.-H. (2016). Cerebrolysin combined with rehabilitation promotes motor recovery in patients with severe motor impairment after stroke. BMC Neurology, 16. https://doi.org/10.1186/s12883-016-0553-z
Recovery from traumatic brain injury
And it seems to improve recovery from TBI as well:

Traumatic brain injury (TBI) is a leading cause of death and
disability for which there is currently no effective drug therapy
available. Because drugs targeting a single TBI pathological pathway
have failed to show clinical efficacy to date, pleiotropic agents with
effects on multiple mechanisms of secondary brain damage could
represent an effective option to improve brain recovery and clinical
outcome in TBI patients... Compared to standard medical care alone
(control group), both doses of Cerebrolysin were associated with
improved clinical outcome scores at 10 days post-TBI in mild patients
and at 10 and 30 days in moderate and severe cases. A dose-dependent
effect of Cerebrolysin on TBI recovery was supported by the
dose-related differences and the significant correlations with
treatment duration observed for outcome measures... In
conclusion, the results of this large retrospective study revealed
that early Cerebrolysin treatment is safe and is associated to
improved TBI outcome.

Muresanu, D., Ciurea, A., Gorgan, R., Gheorghita, E., Florian, S., Stan, H., … Alvarez, A. (2015). A Retrospective, Multi-Center Cohort Study Evaluating the Severity- Related Effects of Cerebrolysin Treatment on Clinical Outcomes in Traumatic Brain Injury. CNS &amp; Neurological Disorders - Drug Targets, 14, 587–599. https://doi.org/10.2174/1871527314666150430162531